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Decision problems for finite special string-rewriting systems that are confluent on some congruence class

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Abstract

The class of decision problems for which finite, special string-rewriting systems that are confluent on some congruence class effectively provide algorithms is compared to the class of decision problems for which finite, monadic, and confluent string-rewriting systems effectively yield algorithms. Among the decision problems solved are the word problem, the power problem, the left-and right-divisibility problems, the finiteness problem, the group problem, the problem of torsion-freeness, the inclusion problem, and the generalized word problem. In particular, it is shown that the technique of linear sentences of Book [7] applies to finite, special string-rewriting systems that are confluent on some congruence class.

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Authors and Affiliations

  1. Fachbereich Mathematik/Informatik, Gesamthochschule Kassel, W-3500, Kassel, Federal Republic of Germany

    Friedrich Otto

  2. Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Louxin Zhang

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  1. Friedrich Otto
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Otto, F., Zhang, L. Decision problems for finite special string-rewriting systems that are confluent on some congruence class. Acta Informatica 28, 477–510 (1991). https://doi.org/10.1007/BF01178585

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