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Decision problems for term rewriting systems and recognizable tree languages

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STACS 91 (STACS 1991)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 480))

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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.

This work was supported in part by the "PRC Mathématiques et Informatique" and ESPRIT2 Working group ASMICS.

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Authors and Affiliations

  1. L.I.F.L, U.R.A 369 C.N.R.S, I.U.T A, Université Lille-Flandres-Artois, 59653, Villeneuve d'Ascq Cedex, France

    Rémi Gilleron

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  1. Rémi Gilleron
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Christian Choffrut Matthias Jantzen

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© 1991 Springer-Verlag Berlin Heidelberg

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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. https://doi.org/10.1007/BFb0020795

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  • DOI: https://doi.org/10.1007/BFb0020795

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-53709-0

  • Online ISBN: 978-3-540-47002-1

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