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The 3 Frenchmen method proves undecidability of the uniform boundedness for single recursive rule ternary DATALOG Programs

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1046))

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Abstract

DATALOG is the language of logic programs without function symbols. It is considered to be the paradigmatic database query language. If it is possible to eliminate the recursion from the program then it is uniformly bounded. We show that the uniform boundedness is undecidable for ternary DATALOG programs containing only one recursive rule, and for linear programs of arity 3. The proof is based on the discovery of, how we call it, Achilles-Turtle machine. It computes the subsequent iterations of a Conway function and is, up to our knowledge, the simplest known universal machine.

The three Frenchmen are Philippe Devienne, Patrick Lebègue and Jean-Christophe Routier. They encoded Conway functions to prove undecidability of the cycle unification problem ([DLR93],[DLR93a]) turning a toy into a powerful tool. My codification of Conway functions is different, but I still feel that this paper would not have been written without their previous work. I also thank Philippe Devienne and Jean-Christophe Routier for helpful discussion.

The paper has been written while the author was visiting Laboratoire d'Informatique Fondamentale in Lille, being supported by CNRS and the University of Lille.

Partly supported by Polish KBN grant 8S 503 022 07.

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Authors and Affiliations

  1. Institute of Computer Science, University of Wrocław, ul. Przesmyckiego 20, 51-165, Wrocław, Poland

    Jerzy Marcinkowski

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  1. Jerzy Marcinkowski
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Claude Puech Rüdiger Reischuk

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© 1996 Springer-Verlag Berlin Heidelberg

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Marcinkowski, J. (1996). The 3 Frenchmen method proves undecidability of the uniform boundedness for single recursive rule ternary DATALOG Programs. In: Puech, C., Reischuk, R. (eds) STACS 96. STACS 1996. Lecture Notes in Computer Science, vol 1046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60922-9_35

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  • DOI: https://doi.org/10.1007/3-540-60922-9_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60922-3

  • Online ISBN: 978-3-540-49723-3

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