Computing #2SAT and #2UNSAT by binary patterns

Authors:
Guillermo De Ita Luna;J. Raymundo Marcial-Romero
Affiliations:
Faculty of Computer Sciences, BUAP, Mexico;Facultad de Ingeniería, UAEM, Mexico
Venue:
MCPR'12 Proceedings of the 4th Mexican conference on Pattern Recognition
Year:
2012

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Abstract

We present some results about the parametric complexity of #2SAT and #2UNSAT, which consist on counting the number of models and falsifying assignments, respectively, for two Conjunctive Forms (2-CF's) . Firstly, we show some cases where given a formula F, #2SAT(F) can be bounded above by considering a binary pattern analysis over its set of clauses. Secondly, since #2SAT(F)=2n-#2UNSAT(F) we show that, by considering the constrained graph GF of F, if GF represents an acyclic graph then, #UNSAT(F) can be computed in polynomial time. To the best of our knowledge, this is the first time where #2UNSAT is computed through its constrained graph, since the inclusion-exclusion formula has been commonly used for computing #UNSAT(F).