论文信息 - Chain Properties of Rule Closures

Chain Properties of Rule Closures

This article presents an introduction to the generalization of the crossed rule approach to the detection of Knuth-Bendix completion procedure divergence. It introduces the closure chains, which are special rule closures constructed by means of particular substitution operations and operators, as a suitable formalism for a progress in this direction. Supporting substitution algebra is developed first, followed by considerations concerning rule closures in general, and concluded by investigation of closure chain properties.

Miki Hermann

[1] Nachum Dershowitz,et al. Termination of Rewriting , 1987, J. Symb. Comput..

[2] Gérard P. Huet,et al. A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm , 1981, J. Comput. Syst. Sci..

[3] Deepak Kapur,et al. On Proving Uniform Termination and Restricted Termination of Rewriting Systems , 1983, SIAM J. Comput..

[4] Max Dauchet. Simulation of Turning Machines by a Left-Linear Rewrite Rule , 1989, RTA.

[5] Miki Hermann,et al. On Nontermination of Knuth-Bendix Algorithm , 1986, ICALP.

[6] James R. Slagle,et al. Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity , 1974, JACM.

[7] Pierre Lescanne,et al. Computer experiments with the REVE term rewriting system generator , 1983, POPL '83.

[8] Pierre Lescanne,et al. Termination of Rewriting Systems by Polynomial Interpretations and Its Implementation , 1987, Sci. Comput. Program..

[9] Hélène Kirchner,et al. Schematization of Infinite Sets of Rewrite Rules Generated by Divergent Completion Processes , 1989, Theor. Comput. Sci..

[10] Paliath Narendran,et al. It is Undecidable Whether the Knuth-Bendix Completion Procedure Generates a Crossed Pair , 1989, STACS.

[11] Jean-Marie Hullot,et al. Canonical Forms and Unification , 1980, CADE.