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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