Abstract

GUILLEN, Carlos; LEMUZ, Rafael  and  AYAQUICA, Irene. Model Counting in the 2μ -3MON Syntactic Class. Comp. y Sist. [online]. 2013, vol.17, n.4, pp.501-513. ISSN 2007-9737.

The counting model problem in Boolean formulas is #P-complete, i.e., there is no known deterministic algorithm in the classical computability model (Turing machine) that makes this count in polynomial time. The difficulty persists even imposing more restrictive conditions on the syntactic classes of Boolean formulas. In this paper we present a treatable family within the syntactical class 2μ-3MON. The identification of this family is done by using the hypergraph associated with simple structures such as chains and cycles. Then, matrix operators acting over these structures are identified; these operators lead to efficient algorithms that perform the model counting on the identified family in linear time for the number of clauses in the instantiated formula; unlike hypergraphic invariant based methods (such as tree width), which perform the count in cubic time.

Keywords : #SAT; syntactic class; hypergraph.