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| In [[formal language]] theory, a [[context-free grammar]] is said to be in '''Chomsky normal form''' (named for [[Noam Chomsky]]) if all of its [[production rule]]s{{disambiguation needed|date=February 2014}} are of the form:
| | Under usual circumstances, the body utilizes glucose or carbohydrates to satisfy its power requirements. In case of individuals following a ketogenic diet, the body has to change over to the stored body fat or dietary fat sources for obtaining energy. Thus, the procedure of fat metabolism involves the generation of vitality inside the form of ATP along with molecules called ketones. Ketosis breathing, moreover called hunger breathing, is regarded as the numerous symptoms of ketosis.<br><br>Drink green tea to feel full between meals. The phytonutrient called EGCG (epigallocatechin gallate) in green tea increases the hormone responsible for making you feel satiated. Drinking green tea daily has long-term benefits too. It can enable avoid storage of excess fat, improve the appetite-regulating hormones and change how your body handles cravings plus metabolizes food.<br><br>Note which the product contains caffeine, that is a stimulant which activates the central nervous system and prompts the launch of vitality boosting chemicals inside the body. Caffeine is addictive plus has negative effects on various organs, yet there is too little caffeine inside the raspberry ketone supplement to result the classic caffeine jitters.<br><br>It is found which overweight persons have harmful dietary patterns. These folks eat too much in comparison to what a typical person would eat throughout food. With the passage of time, the appetite of overweight folks tends to grow. So, without control over the diet, how will you receive the desired fat reduction even after following a daily exercise regime. Diet pills that work without rigorous exercise act as appetite suppressants plus help to get rid of fat in a healthy means.<br><br>Dr. Oz views [http://safedietplansforwomen.com/raspberry-ketones raspberry ketones] as his "number one weight loss miracle in a bottle," he declared on his show recently. This compound, which is made from red raspberries, helps to control adiponectin, which is a hormone that stimulates your body to boost your metabolism. Some say it also suppresses their appetite. The result: your body burns fat more effectively and faster. Think you can just substitute red raspberries?<br><br>If the product does not function for you, it may be returned to the firm and you can get the cash raspberry ketone diet in return. But some people never want to go by this kind of hassle. They want to make certain that the slimming product they buy really functions.<br><br>Become familiar with a food plus whatever they incorporate. We might be ingesting foods that you think are superior for you but are supplying we additional calories.<br><br>Along with portion control plus calorie counting, these supplements helped me get from size 20 pants to size 6-8 and drop from size 2x blouses to small-medium. |
| : <math>A \rightarrow BC</math> or
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| : <math>A \rightarrow \alpha</math> or
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| : <math>S \rightarrow \varepsilon</math>,
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| where <math>A</math>, <math>B</math> and <math>C</math> are nonterminal symbols, <math>\alpha</math> is a [[terminal symbol]] (a symbol that represents a constant value), <math>S</math> is the start symbol, and <math>\varepsilon</math> is the [[empty string]]. Also, neither <math>B</math> nor <math>C</math> may be the start symbol, and the third production rule can only appear if <math>\varepsilon</math> is in <math>L(G)</math>, namely, the language produced by the context-free grammar <math>G</math>.
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| Every grammar in Chomsky normal form is [[Context-free grammar|context-free]], and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form. Several algorithms for performing such a transformation are known. Transformations are described in most textbooks on automata theory, such as Hopcroft and Ullman, 1979.<ref>* John E. Hopcroft, Rajeev Motwani, and Jeffrey D. Ullman. ''Introduction to Automata Theory, Languages, and Computation'', 3rd Edition, Addison-Wesley, 2006. ISBN 0-321-45536-3 ''(see subsection 7.1.5, page 272.)''</ref> As pointed out by Lange and Leiß,<ref>[http://ddi.cs.uni-potsdam.de/InformaticaDidactica/LangeLeiss2009.pdf Lange, Martin and Leiß, Hans. ''To CNF or not to CNF? An Efficient Yet Presentable Version of the CYK Algorithm.'' Informatica Didactica 8, 2009.]</ref> the drawback of these transformations is that they can lead to an undesirable bloat in grammar size. The size of a grammar is the sum of the sizes of its production rules, where the size of a rule is one plus the length of its right-hand side. Using <math>|G|</math> to denote the size of the original grammar <math>G</math>, the size blow-up in the worst case may range from <math>|G|^2</math> to <math>2^{2 |G|}</math>, depending on the transformation algorithm used.
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| ==Alternative definition==
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| Another way to define the Chomsky normal form (e.g., Hopcroft and Ullman 1978,and Hopcroft et al. 2006) is:
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| A [[formal grammar]] is in '''Chomsky reduced form''' if all of its production rules are of the form:
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| : <math>A \rightarrow\, BC</math> or
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| : <math>A \rightarrow\, \alpha</math>,
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| where <math>A</math>, <math>B</math> and <math>C</math> are nonterminal symbols, and <math>\alpha</math> is a [[terminal symbol]]. When using this definition, <math>B</math> or <math>C</math> may be the start symbol. Only those context-free grammars which do not generate the [[empty string]] can be transformed into Chomsky reduced form.
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| ==Converting a grammar to Chomsky Normal Form==
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| # Introduce <math>S_0</math></dt>
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| #: Introduce a new start variable, <math>S_0 </math> and a new rule <math>S_0 \rightarrow S</math> where <math>S </math> is the previous start variable.</dd>
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| # Eliminate all ''<math>\varepsilon</math> rules''</dt>
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| #: <math>\varepsilon</math> rules are rules of the form <math>A \rightarrow \varepsilon</math>, where <math>A \not= S_0</math> and <math>A \in V</math>, where <math>V</math> is the [[Context-free grammar|CFG]]'s variable alphabet.
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| #: Remove every rule with <math>\varepsilon</math> on its right hand side (RHS). For each rule with <math>A</math> in its RHS, add a set of new rules consisting of the different possible combinations of <math>A</math> replaced or not replaced with <math>\varepsilon</math>. If a rule has <math>A</math> as a singleton on its RHS, add a new rule <math>R = A \rightarrow \varepsilon</math> ''unless'' <math>R</math> has already been removed through this process. For example, examine the following grammar <math>G</math>:
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| #:: <math>S \rightarrow AbA \mid B</math>
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| #:: <math>B \rightarrow b \mid c</math>
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| #:: <math>A \rightarrow \varepsilon</math>
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| #:<math>G</math> has one <math>\varepsilon</math> rule. When the <math>A \rightarrow \varepsilon</math> is removed, we get the following:
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| #:: <math>S \rightarrow AbA \mid Ab \mid bA \mid b \mid B</math>
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| #:: <math>B \rightarrow b \mid c</math>
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| #:Notice that we have to account for all possibilities of <math>A \rightarrow \varepsilon</math> and so we actually end up adding 3 rules.
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| # Eliminate all ''unit rules''
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| #:<math>A \rightarrow B; A,B \in V</math>
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| #:After all the <math>\varepsilon</math> rules have been removed, you can begin removing unit rules, or rules whose RHS contains one variable and no terminals (which is inconsistent with CNF).
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| #:: To remove <math>A \rightarrow B</math>
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| #:: <math>\forall B \rightarrow U</math>, where <math>U</math> is a string of variables and terminals, add rule <math>A \rightarrow U</math> unless this is a unit rule which has already been removed.</dd>
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| # Clean up the remaining rules that are not in Chomsky normal form.
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| #: Replace <math>A \rightarrow u_1 u_2 \dotso u_k, k \ge 3, u_1 \in V \cup \Sigma</math> with <math>A \rightarrow u_1 A_1 , A_1 \rightarrow u_2 A_2 , \dotsc , A_{k-2} \rightarrow u_{k-1} u_k</math>, where <math>A_i</math> are new variables.
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| #: If <math>u_i \in \Sigma</math>, replace <math>u_i</math> in above rules with some new variable <math>V_i</math> and add rule <math>V_i \rightarrow u_i</math>.
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| == See also ==
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| *[[Backus-Naur form]]
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| *[[CYK algorithm]]
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| *[[Greibach normal form]]
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| *[[Kuroda normal form]]
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| == Footnotes ==
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| <references />
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| == References ==
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| * John E. Hopcroft and Jeffrey D. Ullman, ''Introduction to Automata Theory, Languages and Computation'', Addison-Wesley Publishing, Reading Massachusetts, 1979. ISBN 0-201-02988-X. ''(See chapter 4.)''
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| * {{cite book
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| | authorlink = Michael Sipser
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| | author = Michael Sipser
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| | year = 1997
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| | title = Introduction to the Theory of Computation
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| | publisher = PWS Publishing
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| | isbn = 0-534-94728-X
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| }} ''(Pages 98–101 of section 2.1: context-free grammars. Page 156.)''
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| * {{cite book
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| | author = John Martin
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| | year = 2003
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| | title = Introduction to Languages and the Theory of Computation
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| | publisher = McGraw Hill
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| | isbn = 0-07-232200-4
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| }} ''(Pages 237–240 of section 6.6: simplified forms and normal forms.)''
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| * {{cite book
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| | authorlink = Michael A. Harrison
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| | author = Michael A. Harrison
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| | year = 1978
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| | title = Introduction to Formal Language Theory
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| | publisher = Addison-Wesley
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| | isbn = 978-0-201-02955-0
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| }} ''(Pages 103–106.)''
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| * Cole, Richard. ''Converting CFGs to CNF (Chomsky Normal Form)'', October 17, 2007. [http://cs.nyu.edu/courses/fall07/V22.0453-001/cnf.pdf (pdf)]
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| * Sipser, Michael. ''Introduction to the Theory of Computation,'' 2nd edition.
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| [[Category:Formal languages]]
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| [[Category:Noam Chomsky]]
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Under usual circumstances, the body utilizes glucose or carbohydrates to satisfy its power requirements. In case of individuals following a ketogenic diet, the body has to change over to the stored body fat or dietary fat sources for obtaining energy. Thus, the procedure of fat metabolism involves the generation of vitality inside the form of ATP along with molecules called ketones. Ketosis breathing, moreover called hunger breathing, is regarded as the numerous symptoms of ketosis.
Drink green tea to feel full between meals. The phytonutrient called EGCG (epigallocatechin gallate) in green tea increases the hormone responsible for making you feel satiated. Drinking green tea daily has long-term benefits too. It can enable avoid storage of excess fat, improve the appetite-regulating hormones and change how your body handles cravings plus metabolizes food.
Note which the product contains caffeine, that is a stimulant which activates the central nervous system and prompts the launch of vitality boosting chemicals inside the body. Caffeine is addictive plus has negative effects on various organs, yet there is too little caffeine inside the raspberry ketone supplement to result the classic caffeine jitters.
It is found which overweight persons have harmful dietary patterns. These folks eat too much in comparison to what a typical person would eat throughout food. With the passage of time, the appetite of overweight folks tends to grow. So, without control over the diet, how will you receive the desired fat reduction even after following a daily exercise regime. Diet pills that work without rigorous exercise act as appetite suppressants plus help to get rid of fat in a healthy means.
Dr. Oz views raspberry ketones as his "number one weight loss miracle in a bottle," he declared on his show recently. This compound, which is made from red raspberries, helps to control adiponectin, which is a hormone that stimulates your body to boost your metabolism. Some say it also suppresses their appetite. The result: your body burns fat more effectively and faster. Think you can just substitute red raspberries?
If the product does not function for you, it may be returned to the firm and you can get the cash raspberry ketone diet in return. But some people never want to go by this kind of hassle. They want to make certain that the slimming product they buy really functions.
Become familiar with a food plus whatever they incorporate. We might be ingesting foods that you think are superior for you but are supplying we additional calories.
Along with portion control plus calorie counting, these supplements helped me get from size 20 pants to size 6-8 and drop from size 2x blouses to small-medium.