Termination orderings for associative-commutative rewriting systems
Journal of Symbolic Computation
Theory of linear and integer programming
Theory of linear and integer programming
Satisfiability of systems of ordinal notations with the subterm property is decidable
Proceedings of the 18th international colloquium on Automata, languages and programming
Handbook of theoretical computer science (vol. B)
Simple LPO constraint solving methods
Information Processing Letters
A total AC-compatible ordering based on RPO
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
Theorem proving with ordering and equality constrained clauses
Journal of Symbolic Computation
Normalized rewriting: an alternative to rewriting modulo a set of equations
Journal of Symbolic Computation
Paramodulation with built-in AC-theories and symbolic constraints
Journal of Symbolic Computation
Solution of the Robbins Problem
Journal of Automated Reasoning
RPO Constraint Solving Is in NP
Proceedings of the 12th International Workshop on Computer Science Logic
Associative-Commutative Deduction with Constraints
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Orderings, AC-theories and Symbolic Constraint Solving
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Paramodulation with Built-In Abelian Groups
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
A Decision Procedure for the Existential Theory of Term Algebras with the Knuth-Bendix Ordering
LICS '00 Proceedings of the 15th Annual IEEE Symposium on Logic in Computer Science
On Ordering Constraints for Deduction with Built-In Abelian Semigroups, Monoids and Groups
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
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It is crucial for the performance of ordered resolution or paramodulation-based deduction systems that they incorporate specialized techniques to work efficiently with standard algebraic theories E. Essential ingredients for this purpose are term orderings that are E-compatible, for the given E, and algorithms deciding constraint satisfiability for such orderings.Here we introduce a uniform technique providing the first such algorithms for some orderings for abelian semigroups, abelian monoids and abelian groups, which we believe will lead to reasonably efficient techniques for practice.Our algorithms are in NP, and hence optimal, since in addition we show that, for any well-founded E-compatible ordering for these E, the constraint satisfiability problem is NP-hard even for conjunctions of inequations.