Unit propagation - Revision history

89.100.142.27: /* Definition */

2014-03-27T15:01:45Z

Definition

← Older revision		Revision as of 17:01, 27 March 2014
Line 1:		Line 1:
	~~{{Confusing\|article\|date=February 2009}}~~		Hi there. Let me start by introducing the writer, her title is Sophia. [http://chorokdeul.co.kr/index.php?document_srl=324263&mid=customer21 free tarot readings] Since I was eighteen I've been working as a bookkeeper but soon my spouse and I will start our personal business. For years he's been residing in Alaska and he doesn't strategy on changing it. Playing badminton is a factor that he is [http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 free psychic readings] completely addicted to.<br><br>Here is my website; phone psychic readings; [https://www.machlitim.org.il/subdomain/megila/end/node/12300 https://www.machlitim.org.il/],

	The '''Davis–Putnam algorithm''' was developed by [[Martin Davis]] and [[Hilary Putnam]] for checking the validity of a [[first-order logic]] formula using a [[Resolution (logic)\|resolution]]-based decision procedure for [[propositional logic]]. Since the set of valid first-order formulas is [[recursively enumerable]] but not [[Recursive set\|recursive]], there ~~exists no general algorithm to solve this problem~~. ~~Therefore,~~ the ~~Davis–Putnam algorithm only terminates on valid formulas. Today~~, ~~the term "Davis-Putnam algorithm"~~ is ~~often used synonymously with the resolution-based propositional decision procedure that is actually only one of the steps of the original algorithm~~.

	~~The procedure is based on~~ [[Herbrand's theorem]], which implies that an [[satisfiable\|unsatisfiable]] formula has an unsatisfiable [[ground instance]], and on the fact that a formula is valid if and only if its negation is unsatisfiable. ~~Taken together, these facts imply that to prove the validity of ''φ'' it is enough to prove that a ground instance of ''¬φ'' is unsatisfiable~~. ~~If ''φ'' is not valid, then the search for an unsatisfiable ground instance will not terminate~~.

	~~The procedure roughly consists of these three parts:~~
	* put the formula in [[prenex]~~] form and eliminate quantifiers~~
	* generate all propositional ground instances, one by one
	* check if each instance is satisfiable

	~~The last part is probably the most innovative one, and works~~ as ~~follows:~~

	* for every variable in the formula
	** for every clause <math>c</math> containing the variable and ~~every clause <math>n</math> containing the negation of the variable~~
	*** [[Resolution (logic)\|resolve]] ''c'' and '~~'n'' and add the resolvent to the formula~~
	** remove all original clauses containing the variable or its negation

	~~At each step, the intermediate formula generated is [[equisatisfiable]] to the original formula, but~~ it ~~does not retain [[Logical equivalence\|equivalence]]. The resolution step leads to a worst-case exponential blow-up in the size of the formula~~. ~~The [[DPLL algorithm]]~~ is a ~~refinement of the propositional satisfiability step of the Davis–Putnam procedure,~~ that ~~requires only a linear amount of memory in the worst case.~~

	~~==See also==~~
	*[~~[Herbrandization]]~~

	~~==References==~~
	* {{cite journal
	~~\|last=Davis~~
	~~\|first=Martin~~
	~~\| coauthors= Putnam, Hilary~~
	~~\| title=A Computing Procedure for Quantification Theory~~
	~~\| journal =[[Journal of the ACM]]~~
	~~\| volume = 7~~
	~~\| issue = 3~~
	~~\| pages = 201–215~~
	~~\| year = 1960~~
	~~\| url =~~ http://~~portal~~.~~acm~~.~~org~~/~~citation~~.~~cfm~~?~~coll~~=~~GUIDE~~&dl=~~GUIDE&id=321034~~
	~~\| doi=10~~.~~1145/321033.321034}}~~
	*{{cite journal
	~~\| last=Beckford~~
	~~\| first=Jahbrill~~
	~~\| coauthors=Logemann, George, and Loveland, Donald~~
	~~\| title=A Machine Program for Theorem Proving~~
	~~\| journal =[~~[~~Communications of the ACM]]~~
	~~\| volume=5~~
	~~\| issue=7~~
	~~\| pages = 394–397~~
	~~\| year=1962~~
	~~\| url=http~~://~~portal~~.~~acm~~.org/~~citation~~.~~cfm?doid=368273~~.~~368557~~
	~~\| doi=10~~.~~1145~~/~~368273.368557}}~~
	* {{cite conference
	~~\| author = R. Dechter~~
	~~\| coauthors = I. Rish~~
	~~\| editor = J. Doyle and E. Sandewall and P. Torasso~~
	~~\| year =~~
	~~\| title = Directional Resolution: The Davis–Putnam Procedure~~, ~~Revisited~~
	~~\| conference =~~
	~~\| booktitle = Principles of Knowledge Representation and Reasoning: Proc. of the Fourth International Conference (KR'94)~~
	~~\| pages = 134–145~~
	~~\| publisher = Starswager18~~
	~~\| url =~~
	~~\| conferenceurl =~~
	}}
	* {{cite book\|author=John Harrison\|title=Handbook of practical logic and automated reasoning\|year=2009\|publisher=Cambridge University Press\|isbn=978-0-521-89957-4\|pages=79–90}}

	~~{{DEFAULTSORT:Davis-Putnam algorithm}}~~
	~~[[Category:Boolean algebra]]~~
	~~[[Category:Constraint programming]]~~
	~~[[Category:Automated theorem proving]]~~


	~~{{formalmethods-stub}}~~

103.21.126.79 at 21:32, 23 May 2013

2013-05-23T21:32:53Z

← Older revision		Revision as of 23:32, 23 May 2013
Line 1:		Line 1:
	~~Hi there. Allow~~ [~~http://www.weddingwall.com.au/groups/easy~~-~~advice~~-for-~~successful-personal-development-today/ free psychic readings~~] ~~me begin by introducing~~ the ~~author~~, ~~her title~~ is ~~Sophia. My day job~~ is ~~an information officer but I've currently utilized for another~~ one. It's ~~not~~ a ~~common thing but what she likes performing~~ is to ~~play domino but she doesn~~'~~t have~~ the ~~time recently~~. ~~For many years he~~'~~s been residing in Alaska~~ and ~~he doesn~~'~~t strategy on altering clairvoyants (~~[http://~~ustanford~~.~~com~~/~~index~~.~~php~~?do=/~~profile-38218/info/~~ http://~~ustanford~~.~~com~~/~~index~~.~~php~~?do=/~~profile-38218/info]) it~~.~~<br><br>Here is my homepage~~ :: ~~tarot readings~~ (~~[http://srncomm.com/blog/2014/08/25/relieve~~-~~that~~-~~stress~~-~~find~~-a-~~new~~-~~hobby/ Suggested Site])~~		{{Confusing\|article\|date=February 2009}}

			The '''Davis–Putnam algorithm''' was developed by [[Martin Davis]] and [[Hilary Putnam]] for checking the validity of a [[first-order logic]] formula using a [[Resolution (logic)\|resolution]]-based decision procedure for [[propositional logic]]. Since the set of valid first-order formulas is [[recursively enumerable]] but not [[Recursive set\|recursive]], there exists no general algorithm to solve this problem. Therefore, the Davis–Putnam algorithm only terminates on valid formulas. Today, the term "Davis-Putnam algorithm" is often used synonymously with the resolution-based propositional decision procedure that is actually only one of the steps of the original algorithm.

			The procedure is based on [[Herbrand's theorem]], which implies that an [[satisfiable\|unsatisfiable]] formula has an unsatisfiable [[ground instance]], and on the fact that a formula is valid if and only if its negation is unsatisfiable. Taken together, these facts imply that to prove the validity of ''φ'' it is enough to prove that a ground instance of ''¬φ'' is unsatisfiable. If ''φ'' is not valid, then the search for an unsatisfiable ground instance will not terminate.

			The procedure roughly consists of these three parts:
			* put the formula in [[prenex]] form and eliminate quantifiers
			* generate all propositional ground instances, one by one
			* check if each instance is satisfiable

			The last part is probably the most innovative one, and works as follows:

			* for every variable in the formula
			** for every clause <math>c</math> containing the variable and every clause <math>n</math> containing the negation of the variable
			*** [[Resolution (logic)\|resolve]] ''c'' and ''n'' and add the resolvent to the formula
			** remove all original clauses containing the variable or its negation

			At each step, the intermediate formula generated is [[equisatisfiable]] to the original formula, but it does not retain [[Logical equivalence\|equivalence]]. The resolution step leads to a worst-case exponential blow-up in the size of the formula. The [[DPLL algorithm]] is a refinement of the propositional satisfiability step of the Davis–Putnam procedure, that requires only a linear amount of memory in the worst case.

			==See also==
			*[[Herbrandization]]

			==References==
			* {{cite journal
			\|last=Davis
			\|first=Martin
			\| coauthors= Putnam, Hilary
			\| title=A Computing Procedure for Quantification Theory
			\| journal =[[Journal of the ACM]]
			\| volume = 7
			\| issue = 3
			\| pages = 201–215
			\| year = 1960
			\| url = http://portal.acm.org/citation.cfm?coll=GUIDE&dl=GUIDE&id=321034
			\| doi=10.1145/321033.321034}}
			*{{cite journal
			\| last=Beckford
			\| first=Jahbrill
			\| coauthors=Logemann, George, and Loveland, Donald
			\| title=A Machine Program for Theorem Proving
			\| journal =[[Communications of the ACM]]
			\| volume=5
			\| issue=7
			\| pages = 394–397
			\| year=1962
			\| url=http://portal.acm.org/citation.cfm?doid=368273.368557
			\| doi=10.1145/368273.368557}}
			* {{cite conference
			\| author = R. Dechter
			\| coauthors = I. Rish
			\| editor = J. Doyle and E. Sandewall and P. Torasso
			\| year =
			\| title = Directional Resolution: The Davis–Putnam Procedure, Revisited
			\| conference =
			\| booktitle = Principles of Knowledge Representation and Reasoning: Proc. of the Fourth International Conference (KR'94)
			\| pages = 134–145
			\| publisher = Starswager18
			\| url =
			\| conferenceurl =
			}}
			* {{cite book\|author=John Harrison\|title=Handbook of practical logic and automated reasoning\|year=2009\|publisher=Cambridge University Press\|isbn=978-0-521-89957-4\|pages=79–90}}

			{{DEFAULTSORT:Davis-Putnam algorithm}}
			[[Category:Boolean algebra]]
			[[Category:Constraint programming]]
			[[Category:Automated theorem proving]]


			{{formalmethods-stub}}

en>ChrisGualtieri: TypoScan Project / General Fixes, typos fixed: , → , using AWB

2012-05-30T02:58:50Z

TypoScan Project / General Fixes, typos fixed: , → , using AWB

New page

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← Older revision		Revision as of 17:01, 27 March 2014
Line 1:		Line 1:
	~~{{Confusing\|article\|date=February 2009}}~~		Hi there. Let me start by introducing the writer, her title is Sophia. [http://chorokdeul.co.kr/index.php?document_srl=324263&mid=customer21 free tarot readings] Since I was eighteen I've been working as a bookkeeper but soon my spouse and I will start our personal business. For years he's been residing in Alaska and he doesn't strategy on changing it. Playing badminton is a factor that he is [http://www.january-yjm.com/xe/index.php?mid=video&document_srl=158289 free psychic readings] completely addicted to.<br><br>Here is my website; phone psychic readings; [https://www.machlitim.org.il/subdomain/megila/end/node/12300 https://www.machlitim.org.il/],

	The '''Davis–Putnam algorithm''' was developed by [[Martin Davis]] and [[Hilary Putnam]] for checking the validity of a [[first-order logic]] formula using a [[Resolution (logic)\|resolution]]-based decision procedure for [[propositional logic]]. Since the set of valid first-order formulas is [[recursively enumerable]] but not [[Recursive set\|recursive]], there ~~exists no general algorithm to solve this problem~~. ~~Therefore,~~ the ~~Davis–Putnam algorithm only terminates on valid formulas. Today~~, ~~the term "Davis-Putnam algorithm"~~ is ~~often used synonymously with the resolution-based propositional decision procedure that is actually only one of the steps of the original algorithm~~.

	~~The procedure is based on~~ [[Herbrand's theorem]], which implies that an [[satisfiable\|unsatisfiable]] formula has an unsatisfiable [[ground instance]], and on the fact that a formula is valid if and only if its negation is unsatisfiable. ~~Taken together, these facts imply that to prove the validity of ''φ'' it is enough to prove that a ground instance of ''¬φ'' is unsatisfiable~~. ~~If ''φ'' is not valid, then the search for an unsatisfiable ground instance will not terminate~~.

	~~The procedure roughly consists of these three parts:~~
	* put the formula in [[prenex]~~] form and eliminate quantifiers~~
	* generate all propositional ground instances, one by one
	* check if each instance is satisfiable

	~~The last part is probably the most innovative one, and works~~ as ~~follows:~~

	* for every variable in the formula
	** for every clause <math>c</math> containing the variable and ~~every clause <math>n</math> containing the negation of the variable~~
	*** [[Resolution (logic)\|resolve]] ''c'' and '~~'n'' and add the resolvent to the formula~~
	** remove all original clauses containing the variable or its negation

	~~At each step, the intermediate formula generated is [[equisatisfiable]] to the original formula, but~~ it ~~does not retain [[Logical equivalence\|equivalence]]. The resolution step leads to a worst-case exponential blow-up in the size of the formula~~. ~~The [[DPLL algorithm]]~~ is a ~~refinement of the propositional satisfiability step of the Davis–Putnam procedure,~~ that ~~requires only a linear amount of memory in the worst case.~~

	~~==See also==~~
	*[~~[Herbrandization]]~~

	~~==References==~~
	* {{cite journal
	~~\|last=Davis~~
	~~\|first=Martin~~
	~~\| coauthors= Putnam, Hilary~~
	~~\| title=A Computing Procedure for Quantification Theory~~
	~~\| journal =[[Journal of the ACM]]~~
	~~\| volume = 7~~
	~~\| issue = 3~~
	~~\| pages = 201–215~~
	~~\| year = 1960~~
	~~\| url =~~ http://~~portal~~.~~acm~~.~~org~~/~~citation~~.~~cfm~~?~~coll~~=~~GUIDE~~&dl=~~GUIDE&id=321034~~
	~~\| doi=10~~.~~1145/321033.321034}}~~
	*{{cite journal
	~~\| last=Beckford~~
	~~\| first=Jahbrill~~
	~~\| coauthors=Logemann, George, and Loveland, Donald~~
	~~\| title=A Machine Program for Theorem Proving~~
	~~\| journal =[~~[~~Communications of the ACM]]~~
	~~\| volume=5~~
	~~\| issue=7~~
	~~\| pages = 394–397~~
	~~\| year=1962~~
	~~\| url=http~~://~~portal~~.~~acm~~.org/~~citation~~.~~cfm?doid=368273~~.~~368557~~
	~~\| doi=10~~.~~1145~~/~~368273.368557}}~~
	* {{cite conference
	~~\| author = R. Dechter~~
	~~\| coauthors = I. Rish~~
	~~\| editor = J. Doyle and E. Sandewall and P. Torasso~~
	~~\| year =~~
	~~\| title = Directional Resolution: The Davis–Putnam Procedure~~, ~~Revisited~~
	~~\| conference =~~
	~~\| booktitle = Principles of Knowledge Representation and Reasoning: Proc. of the Fourth International Conference (KR'94)~~
	~~\| pages = 134–145~~
	~~\| publisher = Starswager18~~
	~~\| url =~~
	~~\| conferenceurl =~~
	}}
	* {{cite book\|author=John Harrison\|title=Handbook of practical logic and automated reasoning\|year=2009\|publisher=Cambridge University Press\|isbn=978-0-521-89957-4\|pages=79–90}}

	~~{{DEFAULTSORT:Davis-Putnam algorithm}}~~
	~~[[Category:Boolean algebra]]~~
	~~[[Category:Constraint programming]]~~
	~~[[Category:Automated theorem proving]]~~


	~~{{formalmethods-stub}}~~