Showing papers on "Conjunctive normal form published in 1984"
14 May 1984
TL;DR: A new decision method is defined for propositional temporal logic of programs to prove some properties of programs such as invariance or eventually because in this logic operators are defined that enable us to represent properties that are valid during all the development of the program or over some parts of the programs.
Abstract: In this paper we define a new decision method for propositional temporal logic of programs Temporal logic appears to be an appropriate tool to prove some properties of programs such as invariance or eventually because in this logic we define operators that enable us to represent properties that are valid during all the development of the program or over some parts of the program
46 citations
TL;DR: A new technique is given for reducing the amount of searching required to solve satisfiability (constraint satisfaction) problems that contain almost pure literals (literals with a small number of occurrences).
Abstract: A new technique, complement searching, is given for reducing the amount of searching required to solve satisfiability (constraint satisfaction) problems. Search trees for these problems often contain subtrees that have approximately the same shape. When this occurs, knowledge that the first subtree does not have a solution can be used to reduce the searching in the second subtree. Only the part of the second subtree which is different from the first needs to be searched. The pure literal rule of the Davis-Putnam procedure is a special case of complement searching. The new technique greatly reduces the amount of searching required to solve conjunctive normal form predicates that contain almost pure literals (literals with a small number of occurrences).
38 citations
14 May 1984
TL;DR: A linear characterization for the solution sets of propositional calculus formulas in conjunctive normal form similar to the basic recurrence relation used to define binomial coefficients is presented.
Abstract: We present a linear characterization for the solution sets of propositional calculus formulas in conjunctive normal form. We obtain recursive definitions for the linear characterization similar to the basic recurrence relation used to define binomial coefficients. As a consequence, we are able to use standard combinatorial and linear algebra techniques to describe properties of the linear characterization.
11 citations
14 May 1984
TL;DR: An algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2(25+e)L is described, and it is shown that the Davis-Putnam procedure satisfies the same upper bound.
Abstract: An algorithm for satisfiability testing in the propositional calculus with a worst case running time that grows at a rate less than 2(.25+e)L is described, where L can be either the length of the input expression or the number of occurrences of literals (i.e., leaves) in it. This represents a new upper bound on the complexity of non-clausal satisfiability testing. The performance is achieved by using lemmas concerning assignments and pruning that preserve satisfiability, together with choosing a “good” variable upon which to recur. For expressions in clause form, it is shown that the Davis-Putnam procedure satisfies the same upper bound.
2 citations
TL;DR: In this paper, a first-order predicate calculus with equality is defined, and a set of formulas in L such that X contains every atomic formula and is closed under substitution of free variables and applications of propositional connectives (not), A (and), v (or).
Abstract: Let L be a first order predicate calculus with equality which has a fixed binary predicate symbol and 5stands for KYl,, Yin> for some n, m. Also 3x, V