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Abstract: The Nelson-Oppen combination method can be used to combine decision procedures for the validity of quantifier-free formulae in firstorder theories with disjoint signatures, provided that the theories to be combined are stably infinite. We show that, even though equational theories need not satisfy this property, Nelson and Oppen's method can be applied, after some minor modifications, to combine decision procedures for the validity of quantifier-free formulae in equational theories.... (Update)
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17: Simplification by cooperating decision procedures (context) - Nelson, Oppen - 1979
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BibTeX entry: (Update)
F. Baader and C. Tinelli. A new approach for combining decision procedures for the word problem, and its connection to the Nelson-Oppen combination method. In Proc. CADE-14 , Springer LNAI 1249, 1997. http://citeseer.ist.psu.edu/baader97new.html More
@inproceedings{ baader97new,
author = "Franz Baader and Cesare Tinelli",
title = "A New Approach for Combining Decision Procedures for the Word Problem, and Its Connection to the {N}elson-{O}ppen Combination Method",
booktitle = "Proceedings of the 14th International Conference on Automated Deduction (Townsville, Australia)",
volume = "1249",
publisher = "Springer-Verlag",
editor = "W.~McCune",
pages = "19--33",
year = "1997",
url = "citeseer.ist.psu.edu/baader97new.html" }
Citations (may not include all citations):634 A machine-oriented logic based on the resolution principle (context) - Robinson - 1965 ACM DBLP
384 Simple word problems in universal algebra (context) - Knuth, Bendix - 1970
170 ACM Transactions on Programming Languages and Systems (context) - Martelli, Montanari et al. - 1982
154 Simplification by cooperating decision procedures (context) - Nelson, Oppen - 1979 ACM DBLP
111 Fast decision procedures based on congruence closure (context) - Nelson, Oppen - 1980 ACM DBLP
83 Counterexamples to termination for the direct sum of term re.. (context) - Toyama - 1987 ACM DBLP
79 the Church-Rosser property for the direct sum of term rewrit.. (context) - Toyama - 1987
49 A new correctness proof of the Nelson--Oppen combination pro.. - Tinelli, Harandi - 1996
44 Combination techniques for non-disjoint equational theories - Domenjoud, Klay et al. - 1994 ACM DBLP
34 Theoretical Computer Science (context) - Oppen, convexity et al. - 1980 ACM
30 Combining matching algorithms: The regular case (context) - Nipkow - 1989 ACM DBLP
26 Combination of unification algorithms (context) - Schmidt-Schauss - 1989 ACM DBLP
11 Cooperation of decision procedures for the satisfiability pr.. - Ringeissen - 1996 DBLP
8 Simple examples of undecidable associative calculi (context) - Matijasevic - 1967
5 Combining symbolic constraint solvers on algebraic domains (context) - Kirchner, Ringeissen - 1994 ACM DBLP
5 Unions of theories and combinations of satisfiability proced.. (context) - Tinelli, Ringeissen - 1996
4 Undecidability of the word problem in the union of theories .. (context) - Domenjoud - 1996
4 First-Order Unification in Combinations of Equational Theori.. (context) - Tid'en - 1986
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