Combining matching algorithms: The regular case

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The problem of combining matching algorithms for equational theories with disjoint signatures is studied. It is shown that the combined matching problem is in general undecidable but that it becomes decidable if all theories are regular. For the case of regular theories an efficient combination algorithm is developed. As part of that development we present a simple algorithm for solving the word problem in the combination of arbitrary equational theories with disjoint signatures.

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This is a revised version of a paper presented at the Third International Conference on Rewriting Techniques and Applications (Chapel Hill, NC) and which appeared in Springer Lec. Notes Comp. Sci. 355. This research was carried out at the Laboratory for Computer Science at MIT with support from NYNEX, NSF grant CCR-8706652, and the Advanced Research Projects Agency of the DoD, monitored by the ONR under contract N00014-83-K-0125.