The homomorphism problem for the free monoid Original Research Article

It is proved to be decidable, for any given finite subset F of X∗ and mapping ϕ:F→X∗, whether or not ϕ can be extended to an (injective) monoid homomorphism ϕ̄:F∗→X∗. As a corollary, an alternative algorithm for the isomorphism problem for the free monoid is also provided: for any given finite subsets F,G of X∗, it is decidable whether or not F∗≃G∗.