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A proof of Ehrenfeucht’s conjecture. (English) Zbl 0602.68066

Ehrenfeucht’s conjecture states that each subset S of a finitely generated free monoid has a finite subset T such that if two endomorphisms of the monoid agree on T, then they agree on S. It is the purpose of this note to verify the conjecture.

MSC:

68Q45 Formal languages and automata
20M05 Free semigroups, generators and relations, word problems
20M35 Semigroups in automata theory, linguistics, etc.
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