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On Conjunctive Normal Form Satisfiability
, 1991
"... This paper focuses on algorithms that solve CSAT (conjunctive normal form satisfiability) by searching for a satisfying truth assignment for the given formula F. We identify four basic ways to improve the basic search procedure: constraint propagators, simplifying transformations, heuristics, and ot ..."
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This paper focuses on algorithms that solve CSAT (conjunctive normal form satisfiability) by searching for a satisfying truth assignment for the given formula F. We identify four basic ways to improve the basic search procedure: constraint propagators, simplifying transformations, heuristics
Homomorphisms of Conjunctive Normal Forms
 Discrete Applied Mathematics
, 2003
"... Abstract We study homomorphisms of propositional formulas in CNF generalizing symmetries considered by Krishnamurthy. If ϕ : H → F is a homomorphism, then unsatisfiability of H implies unsatisfiability of F . Homomorphisms from F to a subset F of F (endomorphisms) are of special interest, since in ..."
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Cited by 11 (3 self)
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Abstract We study homomorphisms of propositional formulas in CNF generalizing symmetries considered by Krishnamurthy. If ϕ : H → F is a homomorphism, then unsatisfiability of H implies unsatisfiability of F . Homomorphisms from F to a subset F of F (endomorphisms) are of special interest, since in such case F and F are satisfiabilityequivalent. We show that smallest subsets F of a formula F for which an endomorphism F → F exists are mutually isomorphic. Furthermore, we study connections between homomorphisms and autark assignments. We introduce the concept of "proof by homomorphism" which is based on the observation that there exist sets Γ of unsatisfiable formulas such that (i) formulas in Γ can be recognized in polynomial time, and (ii) for every unsatisfiable formula F there exist some H ∈ Γ and a homomorphism ϕ : H → F . We identify several sets Γ of unsatisfiable formulas satisfying (i) and (ii) for which proofs by homomorphism w.r.t. Γ and tree resolution proofs can be simulated by each other in polynomial time.
The Representational Power of Conjunctive Normal Form
"... Abstract There is continuing research interest in comparison of the complexity of problems within the class NPComplete. This paper examines the representational power of conjunctive normal form Boolean expressions to establish a proper hierarchy for finite languages, where the language of an expre ..."
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Abstract There is continuing research interest in comparison of the complexity of problems within the class NPComplete. This paper examines the representational power of conjunctive normal form Boolean expressions to establish a proper hierarchy for finite languages, where the language
On Conjunctive Normal Forms With Small Deficiency
, 1999
"... We consider the deficiency ffi (F ) := c(F ) \Gamma n(F ) and the maximal deficiency ffi (F ) := maxF 0 `F ffi (F ) of a set F of clauses (a conjunctive normal form), where c(F ) is the number of clauses in F and n(F ) is the number of variables. Combining ideas from matching and matroid theo ..."
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We consider the deficiency ffi (F ) := c(F ) \Gamma n(F ) and the maximal deficiency ffi (F ) := maxF 0 `F ffi (F ) of a set F of clauses (a conjunctive normal form), where c(F ) is the number of clauses in F and n(F ) is the number of variables. Combining ideas from matching and matroid
Disjunctive and Conjunctive Normal Forms in Fuzzy Logic
"... When performing settheoretical operations, such as intersection and union, on fuzzy sets, one can opt not to consider exact formula, but to leave the results less specific (in particular, intervalvalued) by using both disjunctive and conjunctive representations (normal forms) of the underlying log ..."
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When performing settheoretical operations, such as intersection and union, on fuzzy sets, one can opt not to consider exact formula, but to leave the results less specific (in particular, intervalvalued) by using both disjunctive and conjunctive representations (normal forms) of the underlying
A LinearTime Transformation of Linear Inequalities into Conjunctive Normal Form
, 1996
"... We present a technique that transforms any binary programming problem with integral coefficients to a satisfiability problem of propositional logic in linear time. Preliminary computational experience using this transformation, shows that a pure logical solver can be a valuable tool for solving bina ..."
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Cited by 48 (1 self)
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(1991): 03B05: Classical Propositional Logic; 90C10: Integer Programming. Keywords & Phrases: Linear inequalities, Conjunctive Normal Form, Horn cardinality clauses. 1 Introduction The satisfiability problem of propositional logic (SAT) is considered important in many disciplines
Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms
"... Inductive Logic Programming considers almost exclusively universally quantified theories. To add expressiveness we should consider general prenex conjunctive normal forms which use existential variables. Learning with refinement operators is the most used learning method in ILP. To extend refinement ..."
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Cited by 5 (1 self)
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Inductive Logic Programming considers almost exclusively universally quantified theories. To add expressiveness we should consider general prenex conjunctive normal forms which use existential variables. Learning with refinement operators is the most used learning method in ILP. To extend
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