The homomorphism problem for trace monoids

Abstract

It is proved to be decidable, for any given finite subset F of X ∗ , dependency alphabet ( Y, τ) and mapping ϕ : F → Y ∗ , whether or not ϕ can be extended to a monoid homomorphism ϕ ̃ : F ∗ → M(Y,τ) . This contrasts with the undecidability of the symmetric problem, when we consider the dependency alphabet ( X, τ) instead. Some other particular cases of homomorphism and isomorphism problems among trace monoids are also discussed.