The Inclusion Problem for Unambiguous Rational Trace Languages

Abstract

Given a class $\mathcal{C}$ of languages, the Inclusion Problem for $\mathcal{C}$ consists of deciding whether for $L_{1},L_{2}\in\mathcal{C}$ we have L ₁ ⊆ L ₂.

In this work we prove that the Inclusion Problem is decidable for the class of unambiguous rational trace languages that are subsets of the monoid (((a $_{\rm 1}^{\rm \star}$ b $_{\rm 1}^{\rm \star}$)× c $_{\rm 1}^{\rm \star}$)((a $_{\rm 2}^{\rm \star}$ b $_{\rm 2}^{\rm \star}$)× c $_{\rm 2}^{\rm \star}$))× c $_{\rm 3}^{\rm \star}$.

Partially supported by the Project M.I.U.R. COFIN 2003-2005 “Formal languages and automata: methods, models and applications”