Abstract
We demonstrate that deciding if two terms containing otherwise uninterpreted associative, commutative, and associative-commutative function symbols and commutative variable-binding operators are equal is polynomially equivalent to determining if two graphs are isomorphic. The reductions we use provide insight into this result and suggest polynomial time special cases.
Written at Cornell University under the support of an IBM Fellowship.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Alfred Aho, John Hopcroft, and Jeffrey Ullman. The design and analysis of computer algorithms. Addison-Wesley, 1974.
Leo Bachmair and David A. Plaisted. Associative path orderings. In First International Conference on Rewriting Techniques and Applications, pages 241–254, Dijon, France, 1985.
David A. Basin. Implementing Problem Solving Environments In Constructive Type Theory. PhD thesis, Cornell University, 1990.
Dan Benanav, Deepak Kapur, and Paliath Narendran. Complexity of matching problems. In First International Conference on Rewriting Techniques and Applications, pages 417–429, Dijon, France, 1985.
Kellogg S. Booth and Charles J. Colbourn. Problems Polynomially Equivalent to Graph Isomorphism. Technical Report CS-77-04, University of Waterloo, 1979.
Robert L. Constable et al. Implementing Mathematics with the Nuprl Proof Development System. Prentice Hall, 1986.
Nachum Dershowitz et al. Associative-commutative rewriting. In Eighty International Joint Conference on Artificial Intelligence, pages 940–944, Karlsruhe, West Germany, 1983.
M. Fontet. Automorphismes de graphes et planarite. Asterisque, 73–90, 1976.
Michael R. Garey and David S. Johnson. Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, 1979.
Bernhard Gramlich and Jörg Denzinger. Efficient AC-Matching Using Constraint Propagation. Technical Report SEKI Report SR-88-15, FB Informatik, Universität Kaiserslautern, 1988.
John Hopcroft and J.K. Wong. A linear time algorithm for isomorphism of planar graphs. In Proc. 6th Annual ACM Symposium on Theory of Computing, pages 172–184, 1974.
Gérard Huet and Bernard Lang. Proving and applying program transformations expressed with second-order patterns. Acta Informatica, 31–55, 1978.
J.M. Hullot. Associative-commutative pattern matching. In Proceedings of the IJCAI-79, pages 406–412, Tokyo, Japan, 1979.
David S. Johnson. The NP-completeness column: an ongoing guide. Journal of Algorithms, 9:426–444, 1988.
Deepak Kapur and Paliath Narendran. NP-completeness of the set unification and matching problems. In 8th International Conference On Automated Deduction, pages 489–495, Oxford, UK, 1986.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Basin, D.A. (1990). Equality of terms containing associative-commutative functions and commutative binding operators is isomorphism complete. In: Stickel, M.E. (eds) 10th International Conference on Automated Deduction. CADE 1990. Lecture Notes in Computer Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52885-7_92
Download citation
DOI: https://doi.org/10.1007/3-540-52885-7_92
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52885-2
Online ISBN: 978-3-540-47171-4
eBook Packages: Springer Book Archive