Decision problems for term rewriting systems and recognizable tree languages

  • Rémi Gilleron
Rewriting

DOI: 10.1007/BFb0020795

Part of the Lecture Notes in Computer Science book series (LNCS, volume 480)
Cite this paper as:
Gilleron R. (1991) Decision problems for term rewriting systems and recognizable tree languages. In: Choffrut C., Jantzen M. (eds) STACS 91. STACS 1991. Lecture Notes in Computer Science, vol 480. Springer, Berlin, Heidelberg

Abstract

We study the connections between recognizable tree languages and rewrite systems. We investigate some decision problems. Particularly, let us consider the property (P): a rewrite system S is such that, for every recognizable tree language F, the set of S-normal forms of terms in F is recognizable too. We prove that the property (P) is undecidable. We prove that the existential fragment of the theory of ground term algebras modulo a congruence \(\mathop \leftrightarrow \limits^* E\) generated by a set E of equations such that there exists a finite, noetherian, confluent rewrite system S satisfying (P) with \(\mathop \leftrightarrow \limits^* S = \mathop \leftrightarrow \limits^* E\) is undecidable. Nevertheless, we develop a decision procedure for the validity of linear formulas in a fiagment of such a theory.

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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Rémi Gilleron
    • 1
  1. 1.L.I.F.L, U.R.A 369 C.N.R.S, I.U.T AUniversité Lille-Flandres-ArtoisVilleneuve d'Ascq CedexFrance

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