命題論理におけるβ節充足可能性問題とその解法

抄録

The satisfiability problem (SAT) is one of the important problems in the field of computer science, since it is well known NP-complete problem. The problem is well studied and many valuable results are reported in the literature. We have already proposed IEMSAT algorithm as one of SAT algorithms. Recently, J. N. Hooker made a study of resolution for a set of β clauses. A β clause is a clause that has an additional quantitative condition. The condition is that a β clause is true if and only if at least number of β literals in the clause are true. He also referred to β SAT problem that is SAT consists of β clauses. He, however, did not propose efficient algorithm for it as yet.
This paper intends to present β SAT algorithm ( IEMBSAT ) that is an extended variant of IEMSAT. Some relations between a β clause and a clause are also clarified. Some computational experiments are made to show the effectiveness of IEMBSAT.