A rewriting approach to satisfiability procedures

Information and Computation

Volumn 183, Issue 2, 2003, Pages 140-164

  Armando, Alessandro ^a   Ranise, Silvio ^a,b   Rusinowitch, Michaël ^b  

^a UNIVERSITY OF GENOA   (Italy)

^b INRIA   (France)

Author keywords

Arrays with extensionality; Automated deduction; Decision procedures; Encryption; Equational logic; Finite sets with extensionality; Homomorphism; Lists; Superposition; Term rewriting

Indexed keywords

AUTOMATA THEORY; DECISION THEORY; INFERENCE ENGINES; THEOREM PROVING;

AUTOMATED DEDUCTION; DECISION PROCEDURES; EQUATIONAL LOGIC; FINITE SETS; HOMOMORPHISM; SATISFIABILITY; SUPERPOSITION; TERM REWRITING;

COMPUTABILITY AND DECIDABILITY;

EID: 0038070233     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0890-5401(03)00020-8     Document Type: Article

References (39)

1. A. Armando, S. Ranise, A practical extension mechanism for decision procedures: the case study of universal presburger arithmetic, J. Univ. Comput. Sci. 7 (2) (2001) 124-140.
2. A. Armando, S. Ranise, M. Rusinowitch, Uniform derivation of decision procedures by superposition, in: Computer Science Logic (CSL01), Paris, France, 10-13 September, 2001.
3. L. Bachmair, H. Ganzinger, Rewrite-based equational theorem proving with selection and simplification, J. Logic Comput. 4 (3) (1994) 217-247.
4. L. Bachmair, I. V. Ramakrishnan, A. Tiwari, L. Vigneron, Congruence closure modulo associativity and commutativity, in: Frontiers of Comb. Sys.'s (FroCos'2000), LNCS, 1794, 2000, pp. 245-259.
5. L. Bachmair, A. Tiwari, Abstract congruence closure and specializations, in: D.A. McAllester (Ed.), 17th CADE, LNAI, vol. 1831, 2000, pp. 64-78.
6. D. Basin, H. Ganzinger, Automated complexity analysis based on ordered resolution, J. Assoc. Comput. Mach. 48 (1) (2001) 70-109.
7. N. Bjørner, Integrating decision procedures for temporal verification, Ph.D. thesis, Stanford University, 1999.
8. M. P. Bonacina, On Completion Theorem Proving, January 1991, Thesis of Dottorato di Ricerca, Dipartimento di Scienze dell'Informazione, Università di Milano, Italy.
9. M.P. Bonacina, J. Hsiang, Completion procedures as semidecision procedures, in: M. Okada, S. Kaplan (Eds.), Proc. of the Second International Workshop on Conditional and Typed Term Rewriting Systems (CTRS-90), LNCS, vol. 516, Springer, Berlin, 1991, pp. 206-232.
10. M. P. Bonacina, J. Hsiang, Towards a foundation of completion procedures as semidecision procedures. Theor. Comput. Sci. 146 (July) (1995) 199-242.
11. R.S. Boyer, J.S. Moore, A Computational Logic, Academic Press, New York, 1979.
12. J.R. Burch, D.L. Dill, Automatic verification of pipelined microprocessors control, in: D.L. Dill (Ed.), Proceedings of the Sixth International Conference on Computer-Aided Verification CAV, Standford, California, USA, vol. 818, Springer, Berlin, 1994, pp. 68-80.
13. R. Caferra, N. Peltier, Decision procedures using model building techniques, in: CSL: 9th Workshop on Computer Science Logic, LNCS, vol. 1092, 1995.
14. N. Dershowitz, J.-P. Jouannaud, Rewrite systems, in: J. van Leeuwen (Ed.), Hand. of Theoretical Comp. Science, 1990, pp. 243-320.
15. P.J. Downey, R. Sethi, R.E. Tarjan, Variations on the common subexpression problem, J. ACM 27 (4) (1980) 758-771.
16. H.B. Enderton, A Mathematical Introduction to Logic, Academic Press, New York, 1972.
17. M.J.C. Gordon, T.F. Melham, Introduction to HOL: A Theorem Proving Environment for Higher Order Logic, Cambridge University Press, Cambridge, 1993.
18. J. Goubault, J. Posegga, Bdds and automated deduction, 1994.
19. J. Hsiang, M. Rusinowitch, On word problems in equational theories, in: T. Ottmann (Ed.), Proceedings of the Fourteenth EATCS International Conference on Automata, Languages and Programming, Karlsruhe, West Germany, LNCS, vol. 267, Springer, Berlin, 1987, pp. 54-71.
20. G. Huet, G. Kahn, C. Paulin-Mohring, The Coq Proof Assistant: a tutorial, Technical Report 204, INRIA-Rocquencourt, 1997.
21. G. Huet, A complete proof of correctness of the Knuth-Bendix completion algorithm, J. Comput. Syst. Sci. 23 (1) (1981) 11-21.
22. D. Kapur, Shostak's congruence closure as completion, in: H. Comon (Ed.), Proceedings of the 8th International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science, vol. 1232, Springer, Berlin, 1997.
23. D.E. Knuth, P.E. Bendix, Simple word problems in universal algebra, in: J. Leech (Ed.), Computational Problems in Abstract Algebra, Pergamon Press, Oxford, 1970, pp. 263-297.
24. E. Kounalis, M. Rusinowitch, On word problems in horn theories, JSC 11 (1 & 2) (1991) 113-128.
25. A. Leitsch, Deciding horn classes by hyperresolution, in: CSL: 3rd Workshop on Computer Science Logic, LNCS, 1990.
26. C. Lynch, B. Morawska, Automatic decidability, in: Logic in Computer Science (LICS'02) 26 (2002) 7-18.
27. C. Marché The word problem of ACD-ground theories is undecidable, Int. J. Foundations Comput. Sci. 3 (1) (1992) 81-92.
28. P. Narendran, M. Rusinowitch, Any ground associative-commutative theory has a finite canonical system, in: 4th RTA Conf., Como, Italy, 1991.
29. G. Nelson, Techniques for Program Verification, Technical Report CSL-81-10, Xerox Palo Alto Research Center, June 1981.
30. G. Nelson, D.C. Oppen, Fast decision procedures based on congruence closure, J. ACM 27 (2) (1980) 356-364.
31. G. Nelson, D.C. Oppen, Simplification by Cooperating Decision Procedures, Technical Report STAN-CS-78-652, Stanford CS Department, April 1978.
32. R. Nieuwenhuis, A. Rubio, Paramodulation-based theorem proving, in: A. Robinson, A. Voronkov (Eds.), Hand. of Automated Reasoning, 2001.
33. S. Owre, J.M. Rushby, N. Shankar, PVS: a prototype verification system, in: D. Kapur (Ed.), 11th International Conference on Automated Deduction (CADE), Saratoga, NY, LNAI, vol. 607, Springer, Berlin, 1992, pp. 748-752.
34. D.A. Plaisted, A. Sattler-Klein, Proof lengths for equational completion, Inform. Comput. 125 (2) (1996) 154-170.
35. M. Rusinowitch, Theorem-proving with resolution and superposition, JSC 11 (1 and 2) (1991) 21-50.
36. S. Schulz, System abstract: E 0.61, in: R. Goré, A Leitsch, T. Nipkov (Eds.), Proc. of the 1st IJCAR, Siena, LNAI, vol. 2083, Springer, Berlin, 2001, pp. 370-375.
37. R.E. Shostak, Deciding combination of theories, J. ACM 31 (1) (1984) 1-12.
38. A. Stump, D.L. Dill, C.W. Barrett, J. Levitt, A decision procedure for an extensional theory of arrays, in: LICS'01, 2001.
39. J.D. Ullman, A.V. Aho, J.E. Hopcroft, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.