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On the Complexity of Unification and Disunification in Commutative Idempotent Semigroups
 In Principles and Practice of Constraint Programming  CP97, Third International Conference
, 1997
"... . We analyze the computational complexity of elementary unification and disunification problems for the equational theory ACI of commutative idempotent semigroups. From earlier work, it was known that the decision problem for elementary ACIunification is solvable in polynomial time. We show that th ..."
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Cited by 1 (0 self)
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. We analyze the computational complexity of elementary unification and disunification problems for the equational theory ACI of commutative idempotent semigroups. From earlier work, it was known that the decision problem for elementary ACIunification is solvable in polynomial time. We show
Equational Problems and Disunification
 Journal of Symbolic Computation
, 1989
"... Roughly speaking, an equational problem is a first order formula whose only predicate symbol is =. We propose some rules for the transformation of equational problems and study their correctness in various models. Then, we give completeness results with respect to some “simple ” problems called solv ..."
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Cited by 106 (9 self)
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Roughly speaking, an equational problem is a first order formula whose only predicate symbol is =. We propose some rules for the transformation of equational problems and study their correctness in various models. Then, we give completeness results with respect to some “simple ” problems called solved forms. Such completeness results still hold when adding some control which moreover ensures termination. The termination proofs are given for a “weak ” control and thus hold for the (large) class of algorithms obtained by restricting the scope of the rules. Finally, it must be noted that a byproduct of our method is a decision procedure for the validity in the Herbrand Universe of any
Disunification: a Survey
 Computational Logic: Essays in Honor of Alan
, 1991
"... Solving an equation in an algebra of terms is known as unification. Solving more complex formulas combining equations and involving in particular negation is called disunification. With such a broad definition, many works fall into the scope of disunification. The goal of this paper is to survey the ..."
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Cited by 58 (8 self)
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Solving an equation in an algebra of terms is known as unification. Solving more complex formulas combining equations and involving in particular negation is called disunification. With such a broad definition, many works fall into the scope of disunification. The goal of this paper is to survey
Combining Unification and Disunification Algorithms  Tractable and Intractable Instances
, 1996
"... We consider the problem of combining procedures that decide solvability of (dis)unification problems over disjoint equational theories. Partial answers to the following questions are given: ffl Which properties of the component theories imply intractability in the sense that there cannot be a polyn ..."
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Cited by 2 (1 self)
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We consider the problem of combining procedures that decide solvability of (dis)unification problems over disjoint equational theories. Partial answers to the following questions are given: ffl Which properties of the component theories imply intractability in the sense that there cannot be a
Disunification in ACI1 Theories
, 1999
"... Disunification is the problem of deciding satisfiability of a system of equations and disequations with respect to a given equational theory. In this paper we study the disunification problem in the context of ACI1 equational theories. This problem is of great importance, for instance, for the d ..."
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Cited by 1 (1 self)
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Disunification is the problem of deciding satisfiability of a system of equations and disequations with respect to a given equational theory. In this paper we study the disunification problem in the context of ACI1 equational theories. This problem is of great importance, for instance
Combination Techniques and Decision Problems for Disunification
 Theoretical Computer Science
"... Previous work on combination techniques considered the question of how to combine unification algorithms for disjoint equational theories E 1 ; : : : ; E n in order to obtain a unification algorithm for the union E 1 [ : : : [ E n of the theories. Here we want to show that variants of this method m ..."
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Cited by 21 (6 self)
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Previous work on combination techniques considered the question of how to combine unification algorithms for disjoint equational theories E 1 ; : : : ; E n in order to obtain a unification algorithm for the union E 1 [ : : : [ E n of the theories. Here we want to show that variants of this method
Unification algebras: an axiomatic approach to unification, equation solving and constraint solving
 UNIVERSITAT KAISERSLAUTERN
, 1988
"... Traditionally unification is viewed as solving an equation in an algebra given an explicit construction method for terms and substitutions. We abstract from this explicit term construction methods and give a set of axioms describing unification algebras that consist of objects and mappings, where ob ..."
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Cited by 3 (0 self)
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algebras and unification problems are: Term unification with respect to equational theories and sorts, standard equation solving in mathematics, unification in the λcalculus, constraint solving, disunification, and unification of rational terms. Within this framework we give general purpose unification
Workshop Programme International Workshop on Unification (UNIF’04)
"... UNIF is the main international meeting on unification. Unification is concerned with the problem of identifying given terms, either syntactically or modulo a given logical theory. Syntactic unification is the basic operation of most automated reasoning systems, and unification modulo theories can be ..."
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UNIF is the main international meeting on unification. Unification is concerned with the problem of identifying given terms, either syntactically or modulo a given logical theory. Syntactic unification is the basic operation of most automated reasoning systems, and unification modulo theories can
Unification of Infinite Sets of Terms Schematized by Primal Grammars
 THEORETICAL COMPUTER SCIENCE
, 1996
"... Infinite sets of terms appear frequently at different places in computer science. On the other hand, several practically oriented parts of logic and computer science require the manipulated objects to be finite or finitely representable. Schematizations present a suitable formalism to manipulate fin ..."
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Cited by 24 (3 self)
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or into other rewritebased applications. Primal grammars have a decidable unification problem and ...
Results 1  10
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