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


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


Zbl 0357.94011