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Bottom-up tree pushdown automata and rewrite systems

  • J-L. Coquidé
  • M. Dauchet
  • R. Gilleron
  • S. Vàgvölgyi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 488)

Abstract

Studying connections between term rewrite systems and bottom-up tree pushdown automata (tpda), we complete and generalize results of Gallier, Book and K. Salomaa. We define the notion of tail reduction free rewrite systems (trf rewrite systems). Using the decidability of inductive reducibility (Plaisted), we prove the decidability of the trf property. Monadic rewrite systems of Book, Gallier and K. Salomaa become an obvious particular case of trf rewrite systems. We define also semi-monadic rewrite systems which generalize monadic systems but keep their fair properties. We discuss different notions of bottom-up tree pushdown automata, that can be seen as the algorithmic aspect of classes of problems specified by trf rewrite systems. Especially, we associate a deterministic tpda with any left-linear trf rewrite system.

Key words

Rewrite systems (=term rewrite systems) Church-Rosser (=confluent) systems Noetherian systems Convergent (=noetherian+confluent) systems (Deterministic) tree automaton with pushdown store (Recognizable, Context-free) tree languages 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • J-L. Coquidé
    • 1
  • M. Dauchet
    • 1
  • R. Gilleron
    • 2
  • S. Vàgvölgyi
    • 3
  1. 1.LIFL, URA 369 CNRS, IEEA Université de Lille IVilleneuve d'Ascq CedexFrance
  2. 2.LIFL, URA 369 CNRS, IUT A Université de Lille IVilleneuve d'Ascq CedexFrance
  3. 3.Research Group on Theory of AutomataHungarian Academy of SciencesSzegedHungary

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