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Computations with rational subsets of confluent groups. (English) Zbl 0549.68025
EUROSAM 84, Symbolic and algebraic computation, Proc. int. Symp., Cambridge/Engl. 1984, Lect. Notes Comput. Sci. 174, 207-212 (1984).
[For the entire collection see Zbl 0539.00015.]
This article starts with the observation that if G is a finitely generated group such that the cardinality of any rational (i.e. regular) subset of G can be computed and such that for any two rational subsets R,S of G, $$R\subseteq S$$ is decidable, then the word problem for G, the occurrence problem, and various other problems can be solved in a uniform way. An algorithm proposed by Charles Sims for computation in a free group is reformulated to solve the cardinality and inclusion problems for rational subsets of G when G is a monadic group, and an example indicates that the algorithm may be useful in other cases too. A similar treatment of monadic groups was given previously by R. V. Book [Lect. Notes Comput. Sci. 138, 360-368 (1982; Zbl 0535.68011)].

##### MSC:
 68W30 Symbolic computation and algebraic computation 20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) 68Q45 Formal languages and automata