|
|
| (One intermediate revision by one other user not shown) |
| Line 1: |
Line 1: |
| In [[formal logic]], '''Horn-satisfiability''', or '''HORNSAT''', is the problem of deciding whether a given set of propositional [[Horn clause]]s is satisfiable or not.
| | == Leather UGGs Noira == |
|
| |
|
| A Horn clause is a [[Clause (logic)|clause]] with at most one positive [[literal (mathematical logic)|literal]], called the ''head'' of the clause, and any number of negative literals, forming the ''body'' of the clause. A Horn formula is a [[propositional formula]] formed by [[logical and|conjunction]] of Horn clauses.
| | Sometimes, Entertainment music will come in the form of an already produced song. Movies, Especially teen flicks,[http://www.lehs.org.uk/facebook/list.cfm?page=492 Leather UGGs Noira], Continue to rely heavily on entertainment music. The actual score often plays a secondary role to the myriad of pop hits that appear in a film. <br><br>Scherzinger and Hamilton met in 2007 and began dating in 2008. They broke up in October 2011 but got back together a few months later. Scherzinger and Hamilton reportedly split up because of their long distance relationship (She lives in Los Angeles; He lives in Geneva,[http://www.lehs.org.uk/facebook/list.cfm?page=29 UGG Long Acre London], Switzerland), Their busy work schedules and disagreements over when to start a family,[http://www.lehs.org.uk/facebook/list.cfm?page=580 UGG Australia Outlet Store Bicester], <br><br>Sport often means there is a competitive side to an activity. And horseback riding definitely provides the opportunity for that. Even if it appears that the horse is being judged, The horse is rarely better than the trainer or rider who prepared it. <br><br>I want to add (Indeed he also adds this later) That without free interaction between humans loving relationships are impossible. Humans are highly relational creatures. Therefore this would be disastrous and pointless, Bangalore is home to thousands of expatriates from around the globe. Most have been stationed there by their companies, Though some have been hired and imported by local companies. Others are spouses or children of expats serving in the enormous IT sector, And have become the customers to an ever greater array of services and products aimed at giving foreign residents a taste of home. |
| | |
| The problem of Horn satisfiability is solvable in [[linear time]].<ref>Dowling, W., and Gallier, J., (1984) "Linear-time algorithms for testing the satisfiability of propositional Horn formulae". ''[[Journal of Logic Programming]]'', '''3''', 267-284</ref> A polynomial-time algorithm for Horn satisfiability is based on the rule of [[unit propagation]]: if the formula contains a clause composed of a single literal <math>l</math> (a unit clause), then all clauses containing <math>l</math> (except the unit clause itself) are removed, and all clauses containing <math>\neg l</math> have this literal removed. The result of the second rule may itself be a unit clause, which is propagated in the same manner. If there are no unit clauses, the formula can be satisfied by simply setting all remaining variables negative. The formula is unsatisfiable if this transformation generates a pair of opposite unit clauses <math>l</math> and <math>\neg l</math>. Horn satisfiability is actually one of the "hardest" or "most expressive" problems which is known to be computable in polynomial time, in the sense that it is a [[P-complete|'''P'''-complete]] problem.<ref name="CookNguyen2010">{{cite book|author1=Stephen Cook|author2=Phuong Nguyen|title=Logical foundations of proof complexity|url=http://books.google.com/books?id=2aW2sSlQj_QC&pg=PA224|year=2010|publisher=Cambridge University Press|isbn=978-0-521-51729-4|page=224}}</ref>
| |
| | |
| This algorithm also allows determining a truth assignment of satisfiable Horn formulae: all variables contained in a unit clause are set to the value satisfying that unit clause; all other literals are set to false. The resulting assignment is the minimal model of the Horn formula, that is, the assignment having a minimal set of variables assigned to true, where comparison is made using set containment.
| |
| | |
| Using a linear algorithm for unit propagation, the algorithm is linear in the size of the formula.
| |
| | |
| A generalization of the class of Horn formulae is that of renamable-Horn formulae, which is the set of formulae that can be placed in Horn form by replacing some variables with their respective negation. Checking the existence of such a replacement can be done in linear time; therefore, the satisfiability of such formulae is in P as it can be solved by first performing this replacement and then checking the satisfiability of the resulting Horn formula.<ref>
| |
| {{cite journal
| |
| | last=Chandru
| |
| | first=Vijaya
| |
| | coauthors=Collette R. Coullard, Peter L. Hammer, Miguel Montañez, and Xiaorong Sun
| |
| | title=On renamable Horn and generalized Horn functions
| |
| | journal=Annals of Mathematics and Artificial Intelligence
| |
| | year=2005
| |
| | doi=10.1007/BF01531069
| |
| | volume=1
| |
| | issue=1–4
| |
| | pages=33–47
| |
| }}</ref>
| |
| | |
| The Horn satisfiability problem can also be asked for propositional [[many-valued logic]]s. The algorithms are not usually linear, but some are polynomial; see Hähnle (2001 or 2003) for a survey.<ref>{{cite book|editor=Dov M. Gabbay, Franz Günthner|title=Handbook of philosophical logic|url=http://books.google.com/books?id=_ol81ow-1s4C&pg=PA373|year=2001|publisher=Springer|isbn=978-0-7923-7126-7|page=373|chapter=Advanced many-valued logics|author=Reiner Hähnle|edition=2nd|volume=2}}</ref><ref name="FittingOrlowska2003">{{cite book|editor=Melvin Fitting, Ewa Orlowska|title=Beyond two: theory and applications of multiple-valued logic|year=2003|publisher=Springer|isbn=978-3-7908-1541-2|author=Reiner Hähnle|chapter=Complexity of Many-valued Logics}}</ref>
| |
| | |
| ==See also==
| |
| | |
| * [[Unit propagation]]
| |
| * [[Boolean satisfiability problem]]
| |
| * [[2-satisfiability]]
| |
| | |
| ==References==
| |
| <references />
| |
| | |
| [[Category:Logic in computer science]]
| |
| [[Category:P-complete problems]]
| |
| [[Category:Satisfiability problems]]
| |
| | |
| {{comp-sci-theory-stub}}
| |
Leather UGGs Noira
Sometimes, Entertainment music will come in the form of an already produced song. Movies, Especially teen flicks,Leather UGGs Noira, Continue to rely heavily on entertainment music. The actual score often plays a secondary role to the myriad of pop hits that appear in a film.
Scherzinger and Hamilton met in 2007 and began dating in 2008. They broke up in October 2011 but got back together a few months later. Scherzinger and Hamilton reportedly split up because of their long distance relationship (She lives in Los Angeles; He lives in Geneva,UGG Long Acre London, Switzerland), Their busy work schedules and disagreements over when to start a family,UGG Australia Outlet Store Bicester,
Sport often means there is a competitive side to an activity. And horseback riding definitely provides the opportunity for that. Even if it appears that the horse is being judged, The horse is rarely better than the trainer or rider who prepared it.
I want to add (Indeed he also adds this later) That without free interaction between humans loving relationships are impossible. Humans are highly relational creatures. Therefore this would be disastrous and pointless, Bangalore is home to thousands of expatriates from around the globe. Most have been stationed there by their companies, Though some have been hired and imported by local companies. Others are spouses or children of expats serving in the enormous IT sector, And have become the customers to an ever greater array of services and products aimed at giving foreign residents a taste of home.