Polynomial interpretations are a useful technique for proving termination of term rewrite systems. We show how polynomial interpretations with negative coefficients, like x–1 for a unary function symbol or x–y for a binary function symbol, can be used to extend the class of rewrite systems that can be automatically proved terminating.Proceedings of the 7th International Conference, AISC 2004, Linz, Austria, September 22-24, 2004

Kelsey, Thomas William

Linton, Stephen Alexander

Roney-Dougal, Colva Mary

Polynomial interpretations are a useful technique for proving termination of term rewrite systems. We show how polynomial interpretations with negative coefficients, like x  1 for a unary function symbol or x  y for a binary function symbol, can be used to extend the class of rewrite systems that can be automatically proved terminating

Nao Hirokawa

Aart Middeldorp

CiteSeerX

Polynomial Interpretations with Negative Coefficients

Abstract. Polynomial interpretations are a useful technique for proving termination of term rewrite systems. We show how polynomial interpretations with negative coefficients, like x − 1 for a unary function symbol or x − y for a binary function symbol, can be used to extend the class of rewrite systems that can be automatically proved terminating. 

Polynomial interpretations with negative coefficients

Hirokawa, Nao

Middeldorp, Aart

JAIST Repository

Symmetry-breaking in constraint satisfaction problems is a well-established area of AI research which has recently developed strong interactions with symbolic computation, in the form of computational group theory. GE-trees axe a new conceptual abstraction, providing low-degree polynomial time methods for breaking value symmetries in constraint satisfication problems. In this paper we analyse the structure of symmetry groups of constraint satisfaction problems, and implement several combinations of GE-trees and the classical SBDD method for breaking all symmetries. We prove the efficacy of our techniques, and present preliminary experimental evidence of their practical efficiency.</p

University of St. Andrews - Pure

<strong>New developments in symmetry breaking in search using computational group theory</strong>

We describe proof planning: a technique for both describing the hierarchical structure of proofs and then using this structure to guide proof attempts. When such a proof attempt fails, these failures can be analyzed and a patch formulated and applied. We also describe rippling: a powerful proof method used in proof planning. We pose and answer a number of common questions about proof planning and rippling

Bundy, Alan

Edinburgh Research Explorer