Abstract congruence closure

Journal of Automated Reasoning

Volumn 31, Issue 2, 2003, Pages 129-168

  Bachmair, Leo ^a   Tiwari, Ashish ^b   Vigneron, Laurent ^c  

^a Stony Brook University   (United States)

^b SRI INTERNATIONAL   (United States)

^c UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Associative commutative theories; Congruence closure; Term rewriting

Indexed keywords

ALGORITHMS; COMPUTABILITY AND DECIDABILITY; INFERENCE ENGINES; THEOREM PROVING;

ASSOCIATIVE-COMMUTATIVE THEORIES; CONGRUENCE CLOSURE; TERM REWRITING;

FORMAL LOGIC;

EID: 0346076868     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JARS.0000009518.26415.49     Document Type: Article

References (30)

1. Bachmair, L.: Canonical Equational Proofs, Birkhäuser, Boston, 1991.
2. Bachmair, L. and Dershowitz, N.: Completion for rewriting modulo a congruence, Theoret. Comput. Sci. 67(2 & 3) (Oct. 1989), 173-201.
3. Bachmair, L. and Dershowitz, N.: Equational inference, canonical proofs, and proof orderings, J. ACM 41 (1994), 236-276.
4. Bachmair, L., Ramakrishnan, I., Tiwari, A. and Vigneron, L.: Congruence closure modulo Associativity-Commutativity, in H. Kirchner and C. Ringeissen (eds), Frontiers of Combining Systems, Third International Workshop, FroCoS 2000, Nancy, France, March 2000, Lecture Notes in Artificial Intelligence 1794, Springer, Berlin, 2000, pp. 245-259.
5. Bachmair, L. and Tiwari A.: Abstract congruence closure and specializations, in D. McAllester (ed.), Conference on Automated Deduction, CADE 2000, Pittsburgh, PA, June 2000, Lecture Notes in Artificial Intelligence 1831, Springer, Berlin, 2000, pp. 64-78.
6. Bachmair, L. and Tiwari, A.: Congruence closure and syntactic unification, in C. Lynch and D. Narendran (eds), 14th International Workshop on Unification, 2000.
7. Ballantyne, A. M. and Lankford, D. S.: New decision algorithms for finitely presented commutative semigroups, Comp. Math. Appl. 7 (1981), 159-165.
8. Becker, T. and Weispfenning, V.: Gröbner Bases: A computational Approach to Commutative Algebra, Springer-Verlag, Berlin, 1993.
9. Cardozo, E., Lipton, R. and Meyer, A.: Exponential space complete problems for petri nets and commutative semigroups, in Proc. 8th Ann. ACM Symp on Theory of Computing, 1976, pp. 50-54.
10. Comon, H., Dauchet, M., Gilleron, R., Jacquemard, F., Lugiez, D., Tison, S. and Tommasi, M.: Tree automata techniques and applications. Available on: http://www.grappa.univ-lille3.fr/tata, 1997.
11. Cyrluk, D., Lincoln, P. and Shankar, N.: On Shostak's decision procedure for combination of theories, in M. A. McRobbie and J. Slaney (eds), Proceedings of the 13th Int. Conference on Automated Deduction, Lecture Notes in Comput. Sci. 1104, Springer, Berlin, 1996, pp. 463-477.
12. Dershowitz, N. and Jouannaud, J. P.: Rewrite systems, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science (Vol. B: Formal Models and Semantics), North-Holland, Amsterdam, 1990.
13. Dershowitz, N. and Manna, Z.: Proving termination with multiset orderings, Comm. ACM 22(8) (1979), 465-476.
14. Domenjoud, E. and Klay, F.: Shallow AC theories, in Proceedings of the 2nd CCL Workshop, La Escala, Spain, Sept. 1993.
15. Downey, P. J., Sethi, R. and Tarjan, R. E.: Variations on the common subexpressions problem, J. ACM 27(4) (1980), 758-771.
16. Evans, T.: The word problem for abstract algebras, J. London Math. Soc. 26 (1951), 64-71.
17. Evans, T.: Word problems, Bull. Amer. Math. Soc. 84(5) (1978), 789-802.
18. Kapur, D.: Shostak's congruence closure as completion, in H. Comon (ed.), Rewriting Techniques and Applications, RTA 1997, Sitges, Spain, July 1997, Lecture Notes in Comput. Sci. 1103, Spinger, Berlin, pp. 23-37.
19. Koppenhagen, U. and Mayr, E. W.: An optimal algorithm for constructing the reduced Gröbner basis of binomial ideals, in Y. D. Lakshman (ed.) Proceedings of the International Symposium on Symbolic and Algebraic Computation, 1996, pp. 55-62.
20. Marche, C.: On ground AC-completion, in R. V. Book (ed.), 4th International Conference on Rewriting Techniques and Applications, Lecture Notes in Comput. Sci. 488, Springer, Berlin, 1991, pp. 411-422.
21. Mayr, E. W. and Meyer, A. R.: The complexity of the word problems for commutative semigroups and polynomial ideals, Adv. in Math. 46 (1982), 305-329.
22. Narendran, P. and Rusinowitch, M.: Any ground associative-commutative theory has a finite canonical system, in R. V. Book (ed.) 4th International Conference on Rewriting Techniques and Applications, Lecture Notes in Comput. Sci. 488, Springer, Berlin, 1991, pp. 423-434.
23. Nelson, G. and Oppen, D.: Fast decision procedures based on congruence closure, J. Assoc. Comput. Mach. 27(2) (Apr. 1980), 356-364.
24. Peterson, G. E. and Stickel, M. E.: Complete sets of reductions for some equational theories, J. ACM 28(2) (Apr. 1981), 233-264.
25. Plaisted, D. and Sattler-Klein, A.: Proof lengths for equational completion, Inform. and Comput. 125 (1996), 154-170.
26. Rubio, A. and Nieuwenhuis, R.: A precedence-based total AC-compatible ordering, in C. Kirchner (ed.), Proceedings of the 5 Intl. Conference on Rewriting Techniques and Applications, Lecture Notes in Comput. Sci. 960, Springer, Berlin, 1993, pp. 374-388.
27. Sherman, D. J. and Magnier, N.: Factotum: Automatic and systematic sharing support for systems analyzers, in Proc. TACAS, Lecture Notes in Comput. Sci. 1384, 1998.
28. Shostak, R. E.: Deciding combinations of theories, J. ACM 31(1) (1984), 1-12.
29. Snyder, W.: A fast algorithm for generating reduced ground rewriting systems from a set of ground equations, J. Symbolic Comput. 15(7) (1993).
30. Tiwari, A.: Decision procedures in automated deduction, Ph.D. thesis, State University of New York at Stony Brook, New York, 2000.