The Rational Subset Membership Problem for Groups: A Survey
نویسنده
چکیده
The class of rational subsets of a group G is the smallest class that contains all finite subsets of G and that is closed with respect to union, product and taking the monoid generated by a set. The rational subset membership problem for a finitely generated group G is the decision problem, where for a given rational subset of G and a group element g it is asked whether g ∈ G. This paper presents a survey on known decidability and undecidability results for the rational subset membership problem for groups. The membership problems for finitely generated submonoids and finitely generated subgroups will be discussed as well.
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