Abstract
We hope to have convinced the reader by now, that the extra time spent on the calculations of the measures of the various rules is not wasted, but serves instead as the key factor in the reduction of the size of the search-space. It would seem however that there exists no index function γ, and no sorting strategy Sort, such that γ-Sort (or Sort-γ) be uniformly efficient in all cases. This is the main reason why the software SBR3 has opted for a lexicographic combination of more than one filtration-sorting, giving an appreciable overall efficiency.
Perhaps some future theoretical work will throw more light on this point, as well as on the deletion problem evoked in the previous Section.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
S. Anantharaman, J. Hsiang, Automated Proofs of the Moufang Identities in Alternative Rings, To appear in the J. Automated Reasoning, 1989
S. Anantharaman, J. Mzali, Unfailing Completion Modulo a set of Equations, Research Report, no. 470, LRI-Orsay (Fr.), 1989
S. Anantharaman, J. Hsiang, J. Mzali, SbReve2: A term Rewriting Laboratory with (AC-)Unfailing Completion, RTA (1989)
S. Anantharaman, M-P. Bonacina, Automated Proofs in the Logic of Lukasiewicz, Research Report no. 89-11, LIFO — Orléans.
L. Bachmair, Proof Methods for Equational Theories, Ph.D. Thesis, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA, 1987
N. Dershowitz, Termination of Rewriting, J. Symbolic Computation, Vol 3, pp 59–116, 1987
N. Dershowitz, J.-P. Jouannaud, Rewrite Systems, Handbook of Theoretical Computer Science, Vol B, North-Holland, 1990
J. Hsiang, M. Rusinowitch, On word problems in equational theories, Proc. of the 14th ICALP, Springer-Verlag LNCS, Vol 267, pp 54–71, 1987
D. E. Knuth, P. B. Bendix, Simple Word Problems in Universal Algebras, Computational Problems in Abstract Algebras, Ed. J. Leech, Pergamon Press, pp 263–297, 1970
M. Rusinowitch, Démonstration Automatique par des Téchniques de Réécriture, Thèse d'Etat, Université de Nancy I, 1987
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Anantharaman, S., Andrianarivelo, N. (1990). Heuristical criteria in refutational theorem proving. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1990. Lecture Notes in Computer Science, vol 429. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52531-9_138
Download citation
DOI: https://doi.org/10.1007/3-540-52531-9_138
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52531-8
Online ISBN: 978-3-540-47014-4
eBook Packages: Springer Book Archive