On prefixal one-rule string rewrite systems

Michel Latteux (1) , Yves Roos (1)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189

Prefixal one-rule string rewrite systems are one-rule string rewrite systems for which the left-hand side of the rule is a prefix of the right-hand side of the rule. String rewrite systems induce a transformation over languages: from a starting word, one can associate all its descendants. We prove, in this work, that the transformation induced by a prefixal one-rule rewrite system always transforms a finite language into a context-free language, a property that is surprisingly not satisfied by arbitrary one-rule rewrite systems. We also give here a decidable characterization of the prefixal one-rule rewrite systems whose induced transformation is a rational transduction.

Mots clés: Context free language; One-rule string rewrite system

Domaines: Informatique et langage [cs.CL]

Michel Latteux, Yves Roos. On prefixal one-rule string rewrite systems. Theoretical Computer Science, 2019, 795, pp.240-256. ⟨10.1016/j.tcs.2019.07.004⟩. ⟨hal-02289652⟩