A Canonical Automaton for One-Rule Length-Preserving String Rewrite Systems

International audienceIn this work, we use rearrangements in rewriting positions sequence in order to study precisely the structure of the derivations in one-rule length-preserving string rewrite systems. That yields to the definition of a letter-to-letter transducer that computes the relation induced by a one-rule length-preserving string rewrite system. This transducer can be seen as an automaton over an alphabet A x A. We prove that this automaton is finite if and only if the corresponding relation is rational. We also identify a sufficient condition for the context-freeness of the language L recognized by this automaton and, when this condition is satisfied, we construct a pushdown automaton that recognizes L

On prefixal one-rule string rewrite systems

International audiencePrefixal 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