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On cancellation properties of languages which are supports of rational power series. (English) Zbl 0578.68061
We show two properties of the languages which are supports of noncommutative rational power series: 1. Each such language L possesses a finite test set; that is, there exists a finite language $$K\subset L$$ such that whenever two morphisms into a free monoid coincide on K, then they coincide on L. This is a special case of the Ehrenfeucht conjecture, which was given meanwhile a complete positive (and simple) answer: see e.g. D. Perrin: ”On the solution of Ehrenfeucht’s conjecture” [Bull. Eur. Assoc. Theor. Comput. Sci. 2]. If two complementary languages are both supports, then they are regular.

##### MSC:
 68Q45 Formal languages and automata 16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras) 20M35 Semigroups in automata theory, linguistics, etc.
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