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		<updated>2014-05-22T13:49:14Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Algorithm: &lt;/span&gt;  image added&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 15:49, 22 May 2014&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A lot &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;folks think home improvement &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;not something &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;they &lt;/del&gt;can &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;do. Stories of home improvement failures may make people avoid trying. Home improvement does not have to &lt;/del&gt;be &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a giant pain &lt;/del&gt;in &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the neck&lt;/del&gt;. This &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;article contains some helpful tips &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;get &lt;/del&gt;you &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;started.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Anything simple, like &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lampshade&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;can look and be boring. Brighten up a lamp shade by using stencils and acrylic paint. This will add &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;personal touch&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;making the room reflect your personality&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This &lt;/del&gt;can &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;take a boring room and make it more exciting&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If &lt;/del&gt;you&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;d like &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;re-purpose &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;luggage rack, try transforming it into &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;side table! Simply secure &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sheet &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;glass to &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;top of the rack using permanent adhesive&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Add some books, a pretty lamp&lt;/del&gt;, and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;your side table &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;complete&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Use two-liter bottles that are empty to store things in your kitchen. They are quite useful in that you can see through them and &lt;/del&gt;will &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;hold up well when protecting sugar and flour or other dry goods. You can keep them in &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;freezer, refrigerator, or on &lt;/del&gt;a  &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If you beloved this article and you simply would like to be given &lt;/del&gt;more &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;info regarding &lt;/del&gt;[http://www.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;homeimprovementdaily&lt;/del&gt;.com &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;home improvements diy&lt;/del&gt;] &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;generously visit our page&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;shelf&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;When you need &lt;/del&gt;something &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;all you need &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;do is take &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lid off &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pour&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Chair caning tends to sag over time&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;which is very natural&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;It is relatively simple &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;restore form to your caning&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Take &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sponge and wet the bottom part of your chair&#039;s sagging caning. Be sure that &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;water you&#039;re using is warm. Allow the caning to dry overnight. Continue doing this until your caning is &lt;/del&gt;back &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;to normal&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Don&lt;/del&gt;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;t forget to improve your outdoor living space. Your backyard can make &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;wonderful extension &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;your indoor living area&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a great place for family &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;gather or &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;relax on your own.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;If possible, make home improvements immediately after noticing an issue. You may be able &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;live &lt;/del&gt;with the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;damage &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;happens&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;You don&#039;t want &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;give into this impulse&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A small issue &lt;/del&gt;can &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;rapidly grow into a multifaceted and expensive problem. This may occur more rapidly than you expect&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;When thinking about replacing the cabinets in your home&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;look to wood cabinets. Wood cabinets will last &lt;/del&gt;for &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;years&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;withstanding much wear &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tear. You should invest in cherry&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;maple or oak woods for best results&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;One additional benefit of these woods is that they take stains well. This makes it relatively easy to alter the color scheme of your cabinets&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Plan your next home improvement project&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Avoiding &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;planning until the time you begin &lt;/del&gt;your &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;project can cause indecisiveness &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;many lost dollars due to poor&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;spur-&lt;/del&gt;of-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the-minute decisions&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If you plan in advance&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you will have a much easier &lt;/del&gt;time &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;completing the project&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If your ceiling is starting to leak&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;odds are you need to replace your roof. If you &lt;/del&gt;don&#039;t &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;hurry, you may end up &lt;/del&gt;with a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;disaster on your hands&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Search your area &lt;/del&gt;for &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a high-quality roof &lt;/del&gt;specialist, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and &lt;/del&gt;have &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;them inspect your roof. Do some background research &lt;/del&gt;on &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the roof specialist you want to hire to make sure they are properly qualified&lt;/del&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Always remember, approach each new project &lt;/del&gt;with &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a fresh mind, work on a step-by-step basis, and don&#039;t &lt;/del&gt;be &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;afraid &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;break out &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;your comfort zone by trying something new&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;While the thoughts of home improvement projects may seem terrifying &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you&lt;/del&gt;, it is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;possible &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;successfully complete many tasks &lt;/del&gt;with &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;just &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;little knowledge. If you take the advice in this piece to heart, you will be poised &lt;/del&gt;for &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;true home improvement success&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Accessible at hardware and residence improvement stores, reciprocating saws work equivalent to circular saws, but the blade moves back and forth alternatively of in a full circle. To keep optimal cutting efficiency, reciprocating saw blades must be at least 25mm (1?) longer than the material they are cutting. 1 of the good reciprocating saw makes use &lt;/ins&gt;of is that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it &lt;/ins&gt;can be &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;utilized &lt;/ins&gt;in &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;places that other saws can not reach&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/ins&gt;This &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;implies that if you&#039;re arranging &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;do window operate, you have to have to make positive &lt;/ins&gt;you &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;have &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;excellent reciprocating saw&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;preferably 1 with &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;extended blade&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;before you begin&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Reciprocating saw blades &lt;/ins&gt;can &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;variety in length from two.five to 12 inches&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The assistance manage is a moulded grip (typically rubber) positioned toward the front of reciprocating saws that &lt;/ins&gt;you &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;can use &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;much more accurately guide the saw blade by way of &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;material. The adjustable shoe of &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;reciprocating saw is the plate that rests on the material and offers stability as cutting occurs.  The blade that &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;reciprocating saw makes use &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;essential characteristic that defines its [http://answers.yahoo&lt;/ins&gt;.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com/search/search_result?p=cutting&amp;amp;submit-go=Search+Y!+Answers cutting] capabilities&lt;/ins&gt;, and is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the tool&#039;s primary accessory. I&#039;ve owned this saw a couple years now&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;There &lt;/ins&gt;will &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;also be &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;combo kit (FD02W) that bundles &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;three/8? &lt;/ins&gt; &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Here is &lt;/ins&gt;more &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;information on &lt;/ins&gt;[http://www.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;bestoscillatingtoolreviews&lt;/ins&gt;.com&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/best-rotary-tool-reviews/ ideal Rotary tool accessories&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;stop by the site&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;drill driver with the saw&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;What I mentioned in a further forum is that it is a bit funny how we&#039;ve come to be slaves to battery platforms - significantly much more so than &lt;/ins&gt;something &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;that approached this with corded tools (like Porter Cable Bayonet Jigsaw Blades).  Jigsaws are also made use of for woodworking, but as opposed &lt;/ins&gt;to the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;circular saw, they can be use with thin wood &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;for fine detail perform like trimming thin edges or generating curved cuts&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The LENOX Fleam Ground reciprocating saw blades are obtainable in 6� and 9� lengths and in a version with a tapered plunge cutting tip for faster&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cleaner drywall cutting&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; The reciprocating saw holds a assortment of kinds of blades, ranging from 4 &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;twelve inches lengthy (most are six inches long)&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; However, being &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;energy tool, it moves &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;blade &lt;/ins&gt;back &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and forth considerably more quickly than a human can, thereby cutting a lot more quickly than any manual saw&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;For example, RIDGID&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s model 3030 Fuego reciprocating saw delivers &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;quick ½-inch stroke and weighs only four pounds &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;perform in definitely tight spaces&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; Nevertheless, set against that &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the fact that you have &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;operate with the saw, and if that&#039;s all day, every day, you are going &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;want &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pick a saw &lt;/ins&gt;with the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;weight &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;works ideal for you&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; 1 tip: When buying, lift the saw above your head &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;see if you would be comfy operating like that&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Like pocketknife, one &lt;/ins&gt;can &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fold the blade of this saw&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;These Fein Multimaster kits consist of a FMM 250Q - Variable Speed Tool, a triangle sanding pad with hook &amp;amp; loop fastener but with out holes&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a triangular sanding pad that has holes &lt;/ins&gt;for &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dust extraction, a dust release attachment, a sanding attachment&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;40 sheets of sandpaper (20 each with &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;with out holes), a high speed steel segment saw blade, a grout cutting blade, carbide rasp&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;scraper blade and the universal blade described prior to&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Craft projects often use reciprocating saws&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If you don&#039;t think that these saws can reduce by means of..&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Read Additional what ever it is that you need to reduce, check out &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Lennox saw blade reduce something� site.  Grab &lt;/ins&gt;your &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;reciprocating saw, place in a long blade, &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;make short  Dremel Rotary Tool Reviews work of that tree limb. I&#039;ve cut up trailers, trees&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;fences and even element &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a city bus frame with a low&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;dollar reciprocating saw&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Cheap blades get dull rapid&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;minimizing the effectiveness of the saw and rising your cutting &lt;/ins&gt;time&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.  DeWalt 9 In. ten TPI Demo Reciprocating Blade&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;We have been a bit skeptical about this New Scrolling� type reciprocating saw for two purpose the new scrolling� function seemed odd&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and we typically &lt;/ins&gt;don&#039;t &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;associate Craftsman tools &lt;/ins&gt;with a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;experienced grade&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; This new saw has a seriously hard outer casing and a nice heavy build that just feels right� &lt;/ins&gt;for specialist &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;use. For awkward or really tight areas&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it does not hurt to &lt;/ins&gt;have &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a second five to six amp short-stroke saw &lt;/ins&gt;on &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;hand&lt;/ins&gt;.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This winter I plan to trim back the branches of my four crept myrtle trees &lt;/ins&gt;with &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;this very versatile saw. They appear like they would &lt;/ins&gt;be &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;easy &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;make if you had the right kind &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;saw&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; This question was a superior introduction &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;my investigation&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;but only provided a smaller quantity of detail about the reciprocating saw selection (and &lt;/ins&gt;it is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;difficult &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;know how seriously to take it when it really is the &quot;most enjoyable&quot; choice). Then use the reciprocating saw &lt;/ins&gt;with a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;wood blade only &lt;/ins&gt;for &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;these pieces that are too thick&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;Rocchini</name></author>
	</entry>
	<entry>
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		<title>131.142.24.95: /* Algorithm */</title>
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		<updated>2014-02-24T21:13:46Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Algorithm&lt;/span&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 23:13, 24 February 2014&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In computer science, specifically in the field &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[formal verification]], &#039;&#039;&#039;well-structured transition systems (WSTSs)&#039;&#039;&#039; are a general class &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;infinite state systems for which many verification problems are [[decidable language|decidable]], owing &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the existence of &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;kind of [[well-quasi-ordering|order]] between the states of the system which is compatible with the transitions of &lt;/del&gt;the &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;system&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;WSTS decidability results can be applied &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Petri nets]]&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lossy channel systems&lt;/del&gt;, and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;more&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A lot &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;folks think home improvement is not something that they can do. Stories &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;home improvement failures may make people avoid trying. Home improvement does not have &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;giant pain in &lt;/ins&gt;the &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;neck&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This article contains some helpful tips &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;get you started.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Anything simple&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;like a lampshade&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;can look &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be boring. Brighten up a lamp shade by using stencils and acrylic paint&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This will add &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;personal touch, making the room reflect your personality. This can take &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;boring room and make it more exciting.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If you&#039;d like to re-purpose &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;luggage rack&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;try transforming it into &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;side table! Simply secure a sheet of glass to the top &lt;/ins&gt;of &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the rack using permanent adhesive. Add some books&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a pretty lamp&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;and your side table is complete&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Use two-liter bottles that are empty &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;store things in your kitchen. They are quite useful in that you can see through them and will hold up &lt;/ins&gt;well &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;when protecting sugar and flour &lt;/ins&gt;or &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;other dry goods&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;You can keep them in a freezer, refrigerator&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;or on &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; If you beloved this article and you simply would like to be given more info regarding &lt;/ins&gt;[&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;http://www.homeimprovementdaily.com home improvements diy&lt;/ins&gt;] &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;generously visit our page. shelf. When you need something all you need to do &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;take the lid off and pour.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Chair caning tends to sag over time&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;which is very natural. It &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;relatively simple to restore form to your caning. Take a sponge and wet the bottom part of your chair&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s sagging caning. Be sure that the water you&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;re using is warm. Allow the caning to dry overnight. Continue doing this until your caning is back to normal.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Don&lt;/ins&gt;&#039;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;t forget to improve your outdoor living space&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Your backyard can make &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;wonderful extension to your indoor living area&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;This is &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;great place for family to gather or &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;relax &lt;/ins&gt;on &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;your own&lt;/ins&gt;.&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If possible, make home improvements immediately after noticing an issue. You may be able to live &lt;/ins&gt;with &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the damage &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;happens. You don&#039;t want &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;give into this impulse. A small issue can rapidly grow into a multifaceted and expensive problem. This may occur more rapidly than you expect.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;When thinking about replacing the cabinets in your home&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;look &lt;/ins&gt;to &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;wood cabinets. Wood cabinets will last for years, withstanding much wear &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;tear. You should invest in cherry, maple or oak woods &lt;/ins&gt;for &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;best results. One additional benefit of these woods is &lt;/ins&gt;that &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;they take stains well. This makes it relatively easy to alter the color scheme of your cabinets.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Plan your next home improvement project. Avoiding the planning until the time you begin your project can cause indecisiveness and many lost dollars due to poor&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;spur-of-the-minute decisions. If you plan in advance, you will have a much easier time completing the project.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;If your ceiling &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;starting to leak, odds are you need to replace your roof. If you don&#039;t hurry&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you may end up with a disaster on your hands. Search your area for &lt;/ins&gt;a &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;high-quality roof specialist, &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;have them inspect your roof. Do some background research on the roof specialist you want to hire to make sure they are properly qualified.&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Always remember, approach each new project with a fresh mind&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;work on a step&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;by&lt;/ins&gt;-&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;step basis, and don&#039;t be afraid to break out of your comfort zone by trying something new&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;While the thoughts of home improvement projects may seem terrifying to you&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;it is possible to successfully complete many tasks with just a little knowledge. If you take the advice in this piece to heart&lt;/ins&gt;, &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;you will be poised for true home improvement success&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== Formal definition ==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Recall that &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[well-quasi-ordering]] &amp;lt;math&amp;gt;\leq&amp;lt;/math&amp;gt; on &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;set &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;X&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[quasi-ordering]] (i.e.&lt;/del&gt;, a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[reflexive relation|reflexive]], [[transitive relation|transitive]] [[binary relation]]) such that any infinite sequence &lt;/del&gt;of &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;elements &amp;lt;math&amp;gt;x_0&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;x_1&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;x_2, \ldots&amp;lt;/math&amp;gt;, from &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt; contains an increasing pair &amp;lt;math&amp;gt;x_i \leq x_j&amp;lt;/math&amp;gt; with &amp;lt;math&amp;gt;i &amp;lt; j&amp;lt;/math&amp;gt;&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;The set &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;X&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is said &lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;be &#039;&#039;&#039;&lt;/del&gt;well&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;-quasi-ordered&#039;&#039;&#039;, &lt;/del&gt;or &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;shortly &#039;&#039;&#039;wqo&#039;&#039;&#039;&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;For our purposes&lt;/del&gt;, a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;&#039;&lt;/del&gt;[&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[transition system&lt;/del&gt;]&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;]&#039;&#039; &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a structure &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\mathcal S = \langle S, \rightarrow, \cdots \rangle&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;any set (its elements are called &lt;/del&gt;&#039;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;states&#039;&#039;), and &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\rightarrow \subseteq S \times S&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(its elements are called &lt;/del&gt;&#039;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&#039;transitions&#039;&#039;)&lt;/del&gt;. &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In general &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;transition system may have additional structure like initial states, labels on transitions, accepting states, etc, but they do not concern us here&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A &#039;&#039;&#039;well-structured transition system&#039;&#039;&#039; consists of &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;transition system &amp;lt;math&amp;gt;\langle S, \&lt;/del&gt;to&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;, \leq \rangle&amp;lt;/math&amp;gt;, such that&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &amp;lt;math&amp;gt;\leq \subseteq S \times S&amp;lt;/math&amp;gt; is a well-quasi-ordering &lt;/del&gt;on &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;the set of states&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;\leq&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is upward compatible &lt;/del&gt;with &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;\to&amp;lt;/math&amp;gt;: &lt;/del&gt;that &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;is, for all transitions &amp;lt;math&amp;gt;s_1 \&lt;/del&gt;to &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s_2&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(by this we mean &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;(s_1&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s_2) \in \&lt;/del&gt;to&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;/math&amp;gt;) &lt;/del&gt;and for &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;all &amp;lt;math&amp;gt;t_1&amp;lt;/math&amp;gt; such &lt;/del&gt;that &amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s_1 \leq t_1&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;there exists &lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;t_2&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt; &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;such that &amp;lt;math&amp;gt;t_1 \xrightarrow{*} t_2&amp;lt;/math&amp;gt; (that &lt;/del&gt;is, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;t_2&amp;lt;/math&amp;gt; can be reached from &amp;lt;math&amp;gt;t_1&amp;lt;/math&amp;gt; by &lt;/del&gt;a &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;sequence of zero or more transitions) &lt;/del&gt;and &amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;s_2 \leq t_2&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;.&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== References ==&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* A. Finkel and Ph. Schnoebelen&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[http://www.lsv.ens&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;cachan.fr/Publis/PAPERS/PDF/FinSch&lt;/del&gt;-&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;TCS99&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pdf Well-Structured Transition Systems Everywhere!]&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Theoretical Computer Science 256(1–2)&lt;/del&gt;, &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;pages 63–92, 2001&lt;/del&gt;.&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{comp-sci-theory-stub}}&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Wellfoundedness]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Automata (computation)]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Automata theory]]&lt;/del&gt;&lt;/div&gt;&lt;/td&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-added&quot;&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>131.142.24.95</name></author>
	</entry>
	<entry>
		<id>https://en.formulasearchengine.com/index.php?title=Dykstra%27s_projection_algorithm&amp;diff=26257&amp;oldid=prev</id>
		<title>en&gt;ChrisGualtieri: /* Algorithm */General Fixes using AWB</title>
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		<updated>2013-10-26T02:56:18Z</updated>

		<summary type="html">&lt;p&gt;&lt;span class=&quot;autocomment&quot;&gt;Algorithm: &lt;/span&gt;General Fixes using &lt;a href=&quot;/index.php?title=Testwiki:AWB&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Testwiki:AWB (page does not exist)&quot;&gt;AWB&lt;/a&gt;&lt;/p&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 04:56, 26 October 2013&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l1&quot;&gt;Line 1:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 1:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;My name &lt;/del&gt;is &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Madelaine &lt;/del&gt;(&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;44 years old&lt;/del&gt;) and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;my hobbies &lt;/del&gt;are &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Roller Derby &lt;/del&gt;and &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Golf.&lt;/del&gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&amp;lt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;br&lt;/del&gt;&amp;gt;&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Stop &lt;/del&gt;by &lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;my site &lt;/del&gt;... [http://www.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;homeimprovementdaily&lt;/del&gt;.&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;com home improvements diy&lt;/del&gt;]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;In computer science, specifically in the field of [[formal verification]], &#039;&#039;&#039;well-structured transition systems (WSTSs)&#039;&#039;&#039; are a general class of infinite state systems for which many verification problems are [[decidable language|decidable]], owing to the existence of a kind of [[well-quasi-ordering|order]] between the states of the system which is compatible with the transitions of the system. WSTS decidability results can be applied to [[Petri nets]], lossy channel systems, and more.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== Formal definition ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Recall that a [[well-quasi-ordering]] &amp;lt;math&amp;gt;\leq&amp;lt;/math&amp;gt; on a set &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt; &lt;/ins&gt;is &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a [[quasi-ordering]] &lt;/ins&gt;(&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;i.e., a [[reflexive relation|reflexive]], [[transitive relation|transitive]] [[binary relation]]&lt;/ins&gt;) &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;such that any infinite sequence of elements &amp;lt;math&amp;gt;x_0, x_1, x_2, \ldots&amp;lt;/math&amp;gt;, from &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt; contains an increasing pair &amp;lt;math&amp;gt;x_i \leq x_j&amp;lt;/math&amp;gt; with &amp;lt;math&amp;gt;i &amp;lt; j&amp;lt;/math&amp;gt;. The set &amp;lt;math&amp;gt;X&amp;lt;/math&amp;gt; is said to be &#039;&#039;&#039;well-quasi-ordered&#039;&#039;&#039;, or shortly &#039;&#039;&#039;wqo&#039;&#039;&#039;.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;For our purposes, a &#039;&#039;[[transition system]]&#039;&#039; is a structure &amp;lt;math&amp;gt;\mathcal S = \langle S, \rightarrow, \cdots \rangle&amp;lt;/math&amp;gt;, where &amp;lt;math&amp;gt;S&amp;lt;/math&amp;gt; is any set (its elements are called &#039;&#039;states&#039;&#039;), &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;math&amp;gt;\rightarrow \subseteq S \times S&amp;lt;/math&amp;gt; (its elements &lt;/ins&gt;are &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;called &#039;&#039;transitions&#039;&#039;). In general a transition system may have additional structure like initial states, labels on transitions, accepting states, etc, but they do not concern us here.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;A &#039;&#039;&#039;well-structured transition system&#039;&#039;&#039; consists of a transition system &amp;lt;math&amp;gt;\langle S, \to, \leq \rangle&amp;lt;/math&amp;gt;, such that&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &amp;lt;math&amp;gt;\leq \subseteq S \times S&amp;lt;/math&amp;gt; is a well-quasi-ordering on the set of states.&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* &amp;lt;math&amp;gt;\leq&amp;lt;/math&amp;gt; is upward compatible with &amp;lt;math&amp;gt;\to&amp;lt;/math&amp;gt;: that is, for all transitions &amp;lt;math&amp;gt;s_1 \to s_2&amp;lt;/math&amp;gt; (by this we mean &amp;lt;math&amp;gt;(s_1, s_2) \in \to&amp;lt;/math&amp;gt;) &lt;/ins&gt;and &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;for all &amp;lt;math&amp;gt;t_1&amp;lt;/math&amp;gt; such that &amp;lt;math&amp;gt;s_1 \leq t_1&amp;lt;/math&amp;gt;, there exists &amp;lt;math&amp;gt;t_2&amp;lt;/math&amp;gt; such that &amp;lt;math&amp;gt;t_1 \xrightarrow{*} t_2&amp;lt;/math&amp;gt; (that is, &amp;lt;math&amp;gt;t_2&amp;lt;/math&amp;gt; can be reached from &lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;math&lt;/ins&gt;&amp;gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;t_1&lt;/ins&gt;&amp;lt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;/math&lt;/ins&gt;&amp;gt; by &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;a sequence of zero or more transitions) and &amp;lt;math&amp;gt;s_2 \leq t_2&amp;lt;/math&amp;gt;&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== References ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;* A&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Finkel and Ph&lt;/ins&gt;. &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Schnoebelen, &lt;/ins&gt;[http://www.&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;lsv.ens-cachan.fr/Publis/PAPERS/PDF/FinSch-TCS99.pdf Well-Structured Transition Systems Everywhere!], Theoretical Computer Science 256(1–2), pages 63–92, 2001&lt;/ins&gt;.&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;{{comp-sci-theory-stub}}&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Wellfoundedness]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Automata (computation)]]&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;[[Category:Automata theory]&lt;/ins&gt;]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>en&gt;ChrisGualtieri</name></author>
	</entry>
	<entry>
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		<title>en&gt;Lavaka: adding to :Category:Optimization algorithms and methods</title>
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		<updated>2012-05-04T15:38:41Z</updated>

		<summary type="html">&lt;p&gt;adding to &lt;a href=&quot;/index.php?title=Category:Optimization_algorithms_and_methods&amp;amp;action=edit&amp;amp;redlink=1&quot; class=&quot;new&quot; title=&quot;Category:Optimization algorithms and methods (page does not exist)&quot;&gt;Category:Optimization algorithms and methods&lt;/a&gt;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;My name is Madelaine (44 years old) and my hobbies are Roller Derby and Golf.&amp;lt;br&amp;gt;&amp;lt;br&amp;gt;Stop by my site ... [http://www.homeimprovementdaily.com home improvements diy]&lt;/div&gt;</summary>
		<author><name>en&gt;Lavaka</name></author>
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