Decision problems for finite special string-rewriting systems that are confluent on some congruence class
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 for submonoids generated by regular sets, and the generalized word problem. In particular, it is shown that the technique of linear sentences of \textit{R. Book} [Theor. Comput. Sci. 24, 301-312 (1983; Zbl 0525.68015)] applies to finite, special string-rewriting systems that are confluent on some congruence class.
finite, special string-rewriting systems
scientific article; zbMATH DE number 4146268
scientific article