## Sur les codes synchronisants coupants.(French)Zbl 0542.20046

Quad. Ric. Sci. 109, 7-10 (1981).
If A is a code in a free monoid $$X^*$$ with the property that there is a word $$a_ 0$$ in $$A^*$$ such that every word in $$X^*$$ factors into $$f_ 1f_ 2$$ with $$a_ 0f_ 1$$ and $$f_ 2a_ 0$$ in $$A^*$$, then there are uniquely determined subsets Q and P of $$X^*$$ such that every word in $$X^*$$ has a unique factorization qap with $$q\in Q$$, $$a\in A^*$$, $$p\in P$$. A particular class of codes with this property had been considered by A. Restivo [Discrete Math. 17, 309-316 (1977; Zbl 0357.94011)].
Reviewer: M.Armbrust

### MSC:

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

### Keywords:

free monoid; factorization; codes

Zbl 0357.94011