en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9399)

2013-08-14T01:37:13Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9399)

← Older revision		Revision as of 03:37, 14 August 2013
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	~~Greetings! I am Myrtle Shroyer~~. ~~His spouse doesn't like it the way he does but what he~~ [~~http~~://~~telekomxchange~~.~~com~~/~~groups~~/~~prevent~~-~~infections~~-~~before~~-~~hand~~-~~using-these-tips/ home std test] really likes doing~~ is to ~~do aerobics~~ and ~~he's been over~~ the ~~counter std test doing it for quite~~ a ~~whilst~~. ~~Puerto Rico is exactly where he [http:~~/~~/www~~.~~youporntime~~.~~com/user/KBiaggini std home test~~] and ~~his wife live. Since she was 18 she~~'~~s been operating as~~ a ~~receptionist~~ ~~at home std test but her marketing never std home test arrives.~~<br><br>My [~~http~~:~~//Ohnotheydidnt~~.~~livejournal~~.~~com/49721712~~.~~html web site~~] ~~- at home~~ [~~http~~:~~//www~~.~~Slideshare~~.~~net/realtrafficsource/celebrities-~~with-~~herpes std testing]~~ - ~~[http://happywedding~~.~~lonnieheart~~.~~gethompy~~.~~com/zbxe/wc_apply/372747 navigate to this web-site~~] -		A '''propositional directed acyclic graph (PDAG)''' is a [[data structure]] that is used to represent a [[Boolean function]]. A Boolean function can be represented as a rooted, [[directed acyclic graph]] of the following form:
			* Leaves are labeled with <math>\top</math> (true), <math>\bot</math> (false), or a Boolean variable.
			* Non-leaves are <math>\bigtriangleup</math> (logical and), <math>\bigtriangledown</math> (logical or) and <math>\Diamond</math> (logical not).
			* <math>\bigtriangleup</math>- and <math>\bigtriangledown</math>-nodes have at least one child.
			* <math>\Diamond</math>-nodes have exactly one child.

			Leaves labeled with <math>\top</math> (<math>\bot</math>) represent the constant Boolean function which always evaluates to 1 (0). A leaf labeled with a Boolean variable <math>x</math> is interpreted as the assignment <math>x=1</math>, i.e. it represents the Boolean function which evaluates to 1 if and only if <math>x=1</math>. The Boolean function represented by a <math>\bigtriangleup</math>-node is the one that evaluates to 1, if and only if the Boolean function of all its children evaluate to 1. Similarly, a <math>\bigtriangledown</math>-node represents the Boolean function that evaluates to 1, if and only if the Boolean function of at least one child evaluates to 1. Finally, a <math>\Diamond</math>-node represents the complemenatary Boolean function its child, i.e. the one that evaluates to 1, if and only if the Boolean function of its child evaluates to 0.

			== PDAG, BDD, and NNF ==
			Every '''[[Binary decision diagram\|binary decision diagram (BDD)]]''' and every '''[[Negation normal form\|negation normal form (NNF)]]''' are also a PDAG with some particular properties. The following pictures represent the Boolean function <math>f(x1, x2, x3) = -x1 * -x2 * -x3 + x1 * x2 + x2 * x3</math>:

			{\| align="center"
			\|-
			\| [[File:BDD simple.svg\|thumb\|189px\|BDD for the function f]]
			\| [[File:BDD2pdag.png\|thumb\|189px\|PDAG for the function f obtained from the BDD]]
			\| [[File:BDD2pdag simple.svg\|thumb\|189px\|PDAG for the function f]]
			\|}

			== See also ==
			* [[Data structure]]
			* [[Boolean satisfiability problem]]
			* [[Proposition (mathematics)\|Proposition]]

			== References ==
			* M. Wachter & R. Haenni, "Propositional DAGs: a New Graph-Based Language for Representing Boolean Functions", KR'06, 10th International Conference on Principles of Knowledge Representation and Reasoning, Lake District, UK, 2006.
			* M. Wachter & R. Haenni, "Probabilistic Equivalence Checking with Propositional DAGs", Technical Report iam-2006-001, Institute of Computer Science and Applied Mathematics, University of Bern, Switzerland, 2006.
			* M. Wachter, R. Haenni & J. Jonczy, "Reliability and Diagnostics of Modular Systems: a New Probabilistic Approach", DX'06, 18th International Workshop on Principles of Diagnosis, Peñaranda de Duero, Burgos, Spain, 2006.

			[[Category:Graph data structures]]
			[[Category:Directed graphs]]
			[[Category:Boolean algebra]]

en>ChrisGualtieri: /* Journals */TypoScan Project, typos fixed: , → , using AWB

2012-06-09T15:19:23Z

Journals: TypoScan Project, typos fixed: , → , using AWB

New page

Greetings! I am Myrtle Shroyer. His spouse doesn't like it the way he does but what he [http://telekomxchange.com/groups/prevent-infections-before-hand-using-these-tips/ home std test] really likes doing is to do aerobics and he's been over the counter std test doing it for quite a whilst. Puerto Rico is exactly where he [http://www.youporntime.com/user/KBiaggini std home test] and his wife live. Since she was 18 she's been operating as a receptionist at home std test but her marketing never std home test arrives.<br><br>My [http://Ohnotheydidnt.livejournal.com/49721712.html web site] - at home [http://www.Slideshare.net/realtrafficsource/celebrities-with-herpes std testing] - [http://happywedding.lonnieheart.gethompy.com/zbxe/wc_apply/372747 navigate to this web-site] -

Calogero conjecture - Revision history

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9399)

en>ChrisGualtieri: /* Journals */TypoScan Project, typos fixed: , → , using AWB