On Word Rewriting Systems Having a Rational Derivation
We define four families of word-rewriting systems: the prefix/suffix systems and the left/right systems. The rewriting of prefix systems generalizes the prefix rewriting of systems: a system is prefix (suffix) if a left hand side and a right hand side are overlapping only by prefix (suffix). The rewriting of right systems generalizes the mechanism of transducers: a system is right (left) if a left hand side overlaps a right hand side only on the right (left).
We show that these systems have a rational derivation even if they are not only finite but recognizable. Besides these four families, we give simple systems having a non rational derivation.
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