|
|
| Line 1: |
Line 1: |
| {{DISPLAYTITLE:AC<sup>0</sup>}}
| | Hi there. Allow me start by introducing the author, her title is Sophia. For years she's been residing in Kentucky but her husband wants them to move. Invoicing is my profession. What me and my family love is bungee jumping but I've been using on new issues recently.<br><br>Look into my web site [http://www.aseandate.com/index.php?m=member_profile&p=profile&id=13352970 free online tarot card readings] free [http://ltreme.com/index.php?do=/profile-127790/info/ psychic solutions by lynne] reading ([http://cspl.postech.ac.kr/zboard/Membersonly/144571 Privacy of Data: This tool is built-with and functions-in Client Side JavaScripting, so only your computer will see or process your data input/output.a cool way to improve]) |
| '''AC<sup>0</sup>''' is a [[complexity class]] used in [[circuit complexity]]. It is the smallest class in the [[AC (complexity)|AC]] hierarchy, and consists of all families of circuits of depth O(1) and polynomial size, with unlimited-[[fanin]] [[AND gate]]s and [[OR gate]]s. (We allow [[NOT gate]]s only at the inputs).<ref name=AB118>Arora & Barak (2009) p.118</ref> It thus contains '''NC<sup>0</sup>''', which has only bounded-fanin AND and OR gates.<ref name=AB117>Arora & Barak (2009) p.117</ref>
| |
| | |
| From a [[descriptive complexity]] viewpoint, [[DLOGTIME]]-[[Uniformity (complexity)|uniform]] AC<sup>0</sup> is equal to the descriptive class [[FO (complexity)|FO]]+BIT of all languages describable in first-order logic with the addition of the [[BIT operator]], or alternatively by FO(+, <math>\times</math>), or by Turing machine in the [[LH (complexity)|logarithmic hierarchy]].<ref>*[[Neil Immerman|N. Immerman]] ''Descriptive complexity'' (1999 Springer), page 85.</ref>
| |
| | |
| In 1984 Furst, Saxe, and Sipser showed that calculating the [[parity function|parity]] of an input cannot be decided by any AC<sup>0</sup> circuits, even with non-uniformity.<ref>{{cite journal | zbl=0534.94008 | last1=Furst | first1=Merrick | last2=Saxe | first2=James B. | last3=Sipser | first3=Michael | title=Parity, circuits, and the polynomial-time hierarchy | journal=Math. Syst. Theory | volume=17 | pages=13–27 | year=1984 | issn=0025-5661 }}</ref><ref name=AB287>Arora & Barak (2009) p.287</ref>
| |
| It follows that AC<sup>0</sup> is not equal to [[NC1 (complexity)|NC<sup>1</sup>]], because a family of circuits in the latter class can compute parity.<ref name=AB118/> More precise bounds follow from [[switching lemma]]. Using them, it has been shown that there is an oracle separation between [[polynomial hierarchy|PH]] and [[PSPACE]].
| |
| | |
| Integer addition and subtraction are computable in AC<sup>0</sup>, but multiplication is not (at least, not under the usual binary or base-10 representations of integers).
| |
| | |
| ==References==
| |
| {{reflist}}
| |
| * {{cite book | zbl=1193.68112 | last1=Arora | first1=Sanjeev | author1-link=Sanjeev Arora | last2=Barak | first2=Boaz | title=Computational complexity. A modern approach | publisher=[[Cambridge University Press]] | year=2009 | isbn=978-0-521-42426-4 }}
| |
| | |
| {{ComplexityClasses}}
| |
| | |
| [[Category:Circuit complexity]]
| |
| [[Category:Complexity classes]]
| |
Hi there. Allow me start by introducing the author, her title is Sophia. For years she's been residing in Kentucky but her husband wants them to move. Invoicing is my profession. What me and my family love is bungee jumping but I've been using on new issues recently.
Look into my web site free online tarot card readings free psychic solutions by lynne reading (Privacy of Data: This tool is built-with and functions-in Client Side JavaScripting, so only your computer will see or process your data input/output.a cool way to improve)