Abstract
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 ϕ ̄ :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 ∗ .
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