Abstract
We show that the associative-commutative matching problem is NP-complete; more precisely, the matching problem for terms in which some function symbols are uninterpreted and others are both associative and commutative, is NP-complete. It turns out that the similar problems of associative-matching and commutative-matching are also NP-complete. However, if every variable appears at most once in a term being matched, then the associative-commutative matching problem is shown to have an upper-bound of O (|s| * |t|3), where |s| and |t| are respectively the sizes of the pattern s and the subject t.
Partially supported by the National Science Foundation grant MCS-82-11621.
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8. References
Garey, M.R. and Johnson, D.S., Computers and Intractability, W.H. Freeman, 1979.
Hullot, J.M., „Associative-Commutative Pattern Matching,” Fifth International Joint Conference on Artificial Intelligence, Tokyo, Japan, 1979.
Iwama, K., „On Equations Including String Variables,” Proc. 23rd Ann. Symp. on Foundations of Computer Science, 1982, pp. 226–235.
Kanellakis, P., private communication.
Kapur, D. and Sivakumar, G., „Architecture of and Experiments with RRL, a Rewrite Rule Laboratory,” Proceedings of a NSF Workshop on the Rewrite Rule Laboratory, September 6–9, 1983, General Electric CRD Report, 84GEN004, April, 1984, pp. 33–56.
Knuth, D.E. and Bendix, P.B., „Simple Word Problems in Universal Algebras,” in Computational Problems in Abstract Algebras (ed. J. Leech), Pergamon Press, 1970, pp. 263–297.
Lankford, D.S., „Canonical Inference,” Report ATP-32 Dept. of Mathematics and Computer Sciences, Univ. of Texas, Austin, TX (1975).
Lankford, D.S., and Ballantyne A.M., „Decision Procedures for Simple Equational Theories with Commutative-Associative Axioms: Complete Sets of Commutative-Associative Reductions,” Memo ATP-39, Dept. of Mathematics and Computer Sciences, Univ. of Texas, Austin, TX (1977).
Lankford, D.S., and Ballantyne, A.M., „The Refutation Completeness of Blocked Permutative Narrowing and Resolution,” Fourth Conference on Automated Deduction, 1979.
Papadimitriou, C.H., and Steiglitz, K., Combinatorial Optimization: Algorithms and Complezity, Prentice-Hall, 1982.
Peterson, G.E., and Stickel, M.E., „Complete Sets of Reductions for Some Equational Theories,” Journal of the ACM, Vol. 28, No. 2, pp. 233–264.
Plotkin, G., „Building in Equational Theories,” Machine Intelligence 7 (eds. Meltzer and Michie), pp. 73–90.
Slagle, J., „Automated Theorem Proving with Simplifiers, Commutativity and Associativity,” JACM Vol. 21, 1974, pp. 622–642.
Stickel, M.E., „A Unification Algorithm for Associative-Commutative Functions,” JACM 28 (1980), pp. 423–434.
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Benanav, D., Kapur, D., Narendran, P. (1985). Complexity of matching problems. In: Jouannaud, JP. (eds) Rewriting Techniques and Applications. RTA 1985. Lecture Notes in Computer Science, vol 202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-15976-2_22
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DOI: https://doi.org/10.1007/3-540-15976-2_22
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