scholarly journals The ROBDD Size of Simple CNF Formulas

2003 ◽  
pp. 363-377 ◽  
Author(s):  
Michael Langberg ◽  
Amir Pnueli ◽  
Yoav Rodeh
Keyword(s):  
Cnf Formulas

On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances

2017 ◽  
Vol 18 (3) ◽  
pp. 1-46
Author(s):  
Ronald De Haan ◽  
Iyad Kanj ◽  
Stefan Szeider
Keyword(s):  
Parameterized Complexity ◽  
Cnf Formulas

scholarly journals Generalizations of matched CNF formulas

2004 ◽  
Vol 43 (1-4) ◽  
pp. 223-238 ◽  
Author(s):  
Stefan Szeider
Keyword(s):  
Cnf Formulas

A Linear Time Algorithm for Computing #2SAT for Outerplanar 2-CNF Formulas

2018 ◽  
pp. 72-81 ◽  
Author(s):  
Marco A. López ◽  
J. Raymundo Marcial-Romero ◽  
Guillermo De Ita ◽  
Yolanda Moyao
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Cnf Formulas

NAE-resolution: A new resolution refutation technique to prove not-all-equal unsatisfiability

2020 ◽  
Vol 30 (7) ◽  
pp. 736-751
Author(s):  
Hans Kleine Büning ◽  
P. Wojciechowski ◽  
K. Subramani
Keyword(s):  
Normal Form ◽  
Conjunctive Normal Form ◽  
Principal Result ◽  
Satisfying Assignment ◽  
Boolean Formulas ◽  
Complete Procedure ◽  
Np Complete ◽  
Resolution Refutation ◽  
Original Formula ◽  
Cnf Formulas

AbstractIn this paper, we analyze Boolean formulas in conjunctive normal form (CNF) from the perspective of read-once resolution (ROR) refutation schemes. A read-once (resolution) refutation is one in which each clause is used at most once. Derived clauses can be used as many times as they are deduced. However, clauses in the original formula can only be used as part of one derivation. It is well known that ROR is not complete; that is, there exist unsatisfiable formulas for which no ROR exists. Likewise, the problem of checking if a 3CNF formula has a read-once refutation is NP-complete. This paper is concerned with a variant of satisfiability called not-all-equal satisfiability (NAE-satisfiability). A CNF formula is NAE-satisfiable if it has a satisfying assignment in which at least one literal in each clause is set to false. It is well known that the problem of checking NAE-satisfiability is NP-complete. Clearly, the class of CNF formulas which are NAE-satisfiable is a proper subset of satisfiable CNF formulas. It follows that traditional resolution cannot always find a proof of NAE-unsatisfiability. Thus, traditional resolution is not a sound procedure for checking NAE-satisfiability. In this paper, we introduce a variant of resolution called NAE-resolution which is a sound and complete procedure for checking NAE-satisfiability in CNF formulas. The focus of this paper is on a variant of NAE-resolution called read-once NAE-resolution in which each clause (input or derived) can be part of at most one NAE-resolution step. Our principal result is that read-once NAE-resolution is a sound and complete procedure for 2CNF formulas. Furthermore, we provide an algorithm to determine the smallest such NAE-resolution in polynomial time. This is in stark contrast to the corresponding problem concerning 2CNF formulas and ROR refutations. We also show that the problem of checking whether a 3CNF formula has a read-once NAE-resolution is NP-complete.

scholarly journals BREAKUP: a preprocessing algorithm for satisfiability testing of CNF formulas.

1993 ◽  
Vol 34 (4) ◽  
pp. 602-606 ◽  
Author(s):  
Robert Cowen ◽  
Katherine Wyatt
Keyword(s):  
Cnf Formulas
Sign in / Sign up

Export Citation Format

Share Document