Acta Informatica

, Volume 28, Issue 5, pp 477–510 | Cite as

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

  • Friedrich Otto
  • Louxin Zhang
Article

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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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Friedrich Otto
    • 1
  • Louxin Zhang
    • 2
  1. 1.Fachbereich Mathematik/Informatik, Gesamthochschule KasselKasselFederal Republic of Germany
  2. 2.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada

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