Showing papers on "Conjunctive normal form published in 1978"
01 May 1978
TL;DR: An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.
Abstract: The problem of deciding whether a given propositional formula in conjunctive normal form is satisfiable has been widely studied. I t is known that, when restricted to formulas having only two literals per clause, this problem has an efficient (polynomial-time) solution. But the same problem on formulas having three literals per clause is NP-complete, and hence probably does not have any efficient solution. In this paper, we consider an infinite class of satisfiability problems which contains these two particular problems as special cases, and show that every member of this class is either polynomial-time decidable or NP-complete. The infinite collection of new NP-complete problems so obtained may prove very useful in finding other new NP-complete problems. The classification of the polynomial-time decidable cases yields new problems that are complete in polynomial time and in nondeterministic log space. We also consider an analogous class of problems, involving quantified formulas, which has the property that every member is either polynomial time decidable or complete in polynomial space.
2,108 citations
TL;DR: An exposition of the theory of local algorithms for simplifying the disjunctive normal forms of Boolean functions and the essential nature of all the conditions used in the construction of one of the algorithms is presented, and its majorantness is proved.
Abstract: A BRIEF exposition of the theory of local algorithms for simplifying the disjunctive normal forms of Boolean functions is presented. A proof of the essential nature of all the conditions used in the construction of one of the algorithms is presented, and its majorantness is proved.
23 citations
04 Sep 1978
TL;DR: A logic program is a set of Horn clauses whose conjunction gives an unsatisfiable sentence in clausal form that can be proved using an inference system for first order logic such as that provided by the resolution principle.
Abstract: A logic program is a set of Horn clauses whose conjunction gives an unsatisfiable sentence in clausal form. The sentence's unsatisfiability can be proved using an inference system for first order logic such as that provided by the resolution principle. The interpretation of an input clause set as a program, and of a resolution derivation as a computation, provides the basis of the computational theory of logic programming developed by Kowalski [i~ .
8 citations