N. Dershowitz, J. Hsiang, A. Josephson, and D. Plaisted. Associative-commutative rewriting. In Proc. International Joint Conference on Artificial Intelligence (IJCAI) , pages 940--944, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of # is not valid using a theorem prover. Until the 80 s, interest in SAT was motivated by the possibility of using a SAT solver as the main piece of a theorem prover for first order logic [DP60] Using binary decision diagrams (BDD) Bry92] Other methods including term rewriting [DHJP83, Hsi85] and production systems [Sie87] 3.2 History The history of SAT solvers can be divided into three periods that can be put in parallel with the creation and evolution of computers. Until 1960, SAT solving algorithms were just theoretically described but with no real interest as they could ....

N. Dershowitz, J. Hsiang, N. Josephson, and D. Plaisted. Associative-commutative rewriting. In Proceedings of IJCAI, pages 940--944, 1983.

....methods with built in associativity and commutativity (AC, for short) properties for some of the operators are well known to be crucial in theorem proving and programming. Therefore a lot of work has been done on the development of suitable AC compatible reduction or simplification orderings, like [6, 3, 8, 2, 11, 12, 1, 7, 13, 9]. An essential additional property of the ordering that is needed in order to preserve the completeness of most rewrite based theorem proving techniques (modulo AC) is AC totality, i.e. the totality on (AC different) ground terms. Since the initial attempts, it has always been an aim to obtain ....

N. Dershowitz, J. Hsiang, A. Josephson, and D. Plaisted. Associativecommutative rewriting. In Int. Joint Conf. on Artificial Intelligence, pp. 940-- 944, 1983.

....and term rewriting, a solution to the problem is to build the symmetric axioms into the system, i.e. into the unification process, so that the axioms are not expiic, b needed. Plotkin 72] describes the extension of resolution to resolution with equational unification and [Peterson 81, Dershowitz 83b. Jouannaud 84] describe extensions of term rewriting systems to equational term rewriting systems. Resolution and term rewriting systems are two of the current uses of equational unification, but applications are by no means limited to these two. A review of some ideas for using equational ....

N. Dershowitz, N.A. Josephson, J. Hsiang, and D. Plaisted, "AssociativeCommutative Rewriting," 8th IJCAI, Karlsruhe, West Germany, 1983.

....methods with built in associativity and commutativity (AC) properties for some of the operators are well known to be crucial in theorem proving and programming. Therefore a lot of work has been done on the development of suitable AC compatible reduction or simplification orderings, like [DHJP83,BP85,GL86,BCL87,KSZ90,NR91,Bac92,DP93,RN95,KS97]. An essential additional property of the ordering that is needed in order to preserve the completeness of most rewrite based theorem proving techniques (modulo AC) is AC totality, i.e. the totality on (AC different) ground terms. Since the initial attempts, it has always been an aim to obtain ....

N. Dershowitz, J. Hsiang, A. Josephson, and D. Plaisted. Associativecommutative rewriting. In Int. Joint Conf. on Artificial Intelligence, pp. 940--944, 1983. 25

....heart of a theorem prover for first order logic [DP60] 6. Calculating the number of truth assignments which do not satisfy the formula and comparing this number to 2 P [Iwa89] 7. Other miscellaneous approaches, including BDD graphs [Bry92] solution set enumeration [PR93] term rewriting [DHJP83, Hsi85] and production systems [Sie87] For a brief discussion of incomplete solution strategies, see Section 7.14. 1.4 History Stephen Cook proved that SAT is NP complete in 1971 as part of the paper that defined the notion of NP completeness [Coo71] Other theoretical results pertaining to ....

N. Dershowitz, J. Hsiang, N. Josephson, and D. Plaisted. Associativecommutative rewriting. In Proceedings of IJCAI, pages 940--944, 1983.

....Special AC termination orderings are also needed to show termination of AC rewriting systems. Many commonly used orderings, such as recursive path ordering and lexicographic path ordering, are no longer well founded when flattened terms are used. Several AC termination ordering have been devised [DHJP83, BP85, KSZ90]. We study the problem of AC equational reasoning with a different approach. We propose a procedure called consistent unfailing completion in which only consistent rules and equations are used for critical pair generation and rewriting. A consistent unfailing completion procedure can be regarded ....

Nachum Dershowitz, J. Hsiang, N. Josephson, and David A. Plaisted. Associative-commutative rewriting. In Proceedings of the Eighth International Joint Conference on Artificial Intelligence, pages 940--944, August 1983.

....SAT problem on the assumption that P 6= NP . On the other hand, the SAT problem is fundamental in solving many practical problems in logic programming, inference, machine learning, and constraint satisfaction. Many practical algorithms and approaches have been developed to solve the SAT problem. [18, 46, 74, 53, 63, 92]. Among many algorithms and techniques proposed, the Davis Putnam algorithm [17] in essence a resolution procedure, has been a major practical method for solving the SAT problem. The Davis Putnam algorithm is able to determine satisfiability as well as unsatisfiability. However it is not ....

....to determine a solution. One straightforward way to solve an instance of SAT is to enumerate all possible truth assignments and check to see if one satisfies the formula. Many improved techniques, such as consistency algorithms [61] backtracking algorithms [5, 8, 10, 57, 67] term rewriting [18, 46], production system [76] multivalued logic [74] Binary Decision Diagrams [9, 2] chip and conquer [26] resolution 8 ....

N. Dershowitz, J. Hsiang, N. Josephson, and D. Plaisted. Associative-commutative rewriting. In Proceedings of IJCAI, pages 940--944, 1983.

....search and inference procedures. One straightforward way to solve the SAT problem is to enumerate all possible truth assignments to see if one satisfies the formula. Many improved techniques, such as consistency algorithms [47, 76] backtracking algorithms [4, 7, 9, 71, 83] term rewriting [20, 60], production system [96] multi valued logic [94] Binary Decision Diagrams [2, 8] chip and conquer [29] independent set al..gorithm [64] and resolution and regular resolution [30, 74, 79, 88, 103, 106] have been proposed. Specific versions of resolution principle include Davis Putnam algorithm ....

N. Dershowitz, J. Hsiang, N. Josephson, and D. Plaisted. Associative-commutative rewriting. In Proceedings of IJCAI, pages 940--944, 1983.

....methods with built in associativity and commutativity(AC) properties for some of the operators are well known to be crucial in theorem proving and programming. Therefore a lot of work has been done on the development of suitable AC compatible reduction or simplification orderings, like [DHJP83, BP85, GL86, BCL87, KSZ90, NR91, Bac92, DP93, RN95, KS97]. An essential additional property of the ordering that is needed in order to preserve the completeness of most rewrite based theorem proving techniques (modulo AC) is AC totality, i.e. the totality on (AC different) ground terms. Since the initial attempts, it has always been an aim to obtain ....

N. Dershowitz, J. Hsiang, A. Josephson, and D. Plaisted. Associativecommutative rewriting. In Int. Joint Conference on Artificial Inteligence, pages 940--944, 1983.

....Work Many algorithms and approaches have been developed for the SAT problem [23, 63] One straightforward way to solve the SAT problem is to enumerate all possible truth assignments to see if one satisfies the formula. Among many techniques proposed, such as backtracking search, term rewriting [8, 38], production system [72] multi valued logic [70] resolution and its variations [60, 65, 84] resolution is the most widely used method. A resolution based approach is not able to handle certain large size inference problems. The Davis Putnam algorithm, in essence a resolution procedure, has been ....

N. Dershowitz, J. Hsiang, N. Josephson, and D. Plaisted. Associative-commutative rewriting. In Proceedings of IJCAI, pages 940--944, 1983.

....Especially interesting because of its many practical applications is the case when the equational theory is associativity and commutativity (AC) for some of the operators. Therefore a lot of work has been done on the development of suitable AC compatible reduction or simplification orderings, like [DHJP83, BP85, GL86, BCL87, KSZ90, Bac92]. An essential additional property of the ordering that is needed in order to preserve the completeness of most rewrite based theorem proving techniques for first order clauses (modulo AC) is its totality on (AC different) ground terms. Such a total ordering was finally found by Narendran and ....

N. Dershowitz, J. Hsiang, A. Josephson, and D. Plaisted. Associative-commutative rewriting. In Int. Joint Conference on Artificial Inteligence, pages 940--944, 1983.

....methods with built in associativity and commutativity (AC) properties for some of the operators are well known to be crucial in theorem proving and programming. Therefore a lot of work has been done on the development of suitable AC compatible reduction or simplification orderings, like [DHJP83, BP85, GL86, BCL87, KSZ90, NR91, Bac92, DP93, RN95, KS97]. An essential additional property of the ordering that is needed in order to preserve the completeness of most rewrite based theorem proving techniques (modulo AC) is AC totality, i.e. the totality on (AC different) ground terms. Since the initial attempts, it has always been an aim to obtain ....

N. Dershowitz, J. Hsiang, A. Josephson, and D. Plaisted. Associativecommutative rewriting. In Int. Joint Conference on Artificial Inteligence, pages 940--944, 1983.

....Special AC termination orderings are also needed to show termination of AC rewriting systems. Many commonly used orderings, such as recursive path ordering and lexicographic path ordering, are no longer well founded when flattened terms are used. Several AC termination ordering have been devised [ Dershowitz et al. 1983; Bachmair and Plaisted, 1985; Kapur et al. 1990 ] We study the problem of AC equational reasoning with a different approach. We propose a procedure called consistent unfailing completion in which only consistent rules and equations are used for critical pair generation and rewriting. A ....

Nachum Dershowitz, J. Hsiang, N. Josephson, and David A. Plaisted. Associativecommutative rewriting. In Proceedings of the Eighth International Joint Conference on Artificial Intelligence, pages 940--944, August 1983.

....used. See [Lankford, 1979] and [Ben Cherifa and Lescanne, 1987] Path orderings have been commonly used in theorem provers, even for AC rewriting (see the discussion in [Bjorner, 1982, page 350] despite the fact that they do not establish termination in the AC case (see the counterexamples in [Dershowitz et al. 1983]) Extensions of path orderings that do handle associative and commutative functions properly ( Bachmair and Plaisted, 1985] for example) have been proposed, most recently in [Kapur et al. 1990] However, the ordering of [Kapur et al. 1990] is difficult to implement, because it requires many ....

N. Dershowitz, J. Hsiang, N. A. Josephson and D. A. Plaisted. Associative-commutative rewriting. In Proceedings of the Eighth International Joint Conference on Artificial Intelligence, Karlsruhe, West Germany, pages 940--944, 1983.

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N. Dershowitz, J. Hsiang, A. Josephson, and D. Plaisted. Associative-commutative rewriting. In Proc. International Joint Conference on Artificial Intelligence (IJCAI) , pages 940--944, 1983.

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Nachum Dershowitz et al. Associative-commutative rewriting. In Eighty International Joint Conference on Artificial Intelligence, pages 940--944, Karlsruhe, West Germany, 1983.

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