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International Conference on Rewriting Techniques and Applications

RTA 1998: Rewriting Techniques and Applications pp 181–195Cite as

The decidability of simultaneous rigid E-unification with one variable

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1379))

Abstract

We show that simultaneous rigid E-unification, or SREU for short, is decidable and in fact EXPTIME-complete in the case of one variable. This result implies that the ∀*∃∀* fragment of intuitionistic logic with equality is decidable. Together with a previous result regarding the undecidability of the ∃∃-fragment, we obtain a complete classification of decidability of the prenex fragment of intuitionistic logic with equality, in terms of the quantifier prefix. It is also proved that SREU with one variable and a constant bound on the number of rigid equations is P-complete.

Supported by grants from the Swedish Royal Academy of Sciences, INTAS and NUTEK.

Partially supported by grants from NSF, ONR and the Faculty of Science and Technology of Uppsala University.

Supported by the NSF grants CCR-9404930 and INT-9401087.

Supported by a TFR grant.

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Author information

Authors and Affiliations

  1. Computing Science Department, Uppsala University, P.O. Box 311, S-751 05, Uppsala, Sweden

    Anatoli Degtyarev & Andrei Voronkov

  2. EECS Department, University of Michigan, 48109-2122, Ann Arbor, MI, USA

    Yuri Gurevich

  3. Department of Computer Science, University at Albany - SUNY, 12222, Albany, New York, USA

    Paliath Narendran

  4. Max-Planck-Institut für Informatik, Im Stadtwald, 66123, Saarbrücken, Germany

    Margus Veanes

Authors
  1. Anatoli Degtyarev
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  2. Yuri Gurevich
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  3. Paliath Narendran
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  4. Margus Veanes
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  5. Andrei Voronkov
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Tobias Nipkow

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© 1998 Springer-Verlag

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Degtyarev, A., Gurevich, Y., Narendran, P., Veanes, M., Voronkov, A. (1998). The decidability of simultaneous rigid E-unification with one variable. In: Nipkow, T. (eds) Rewriting Techniques and Applications. RTA 1998. Lecture Notes in Computer Science, vol 1379. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052370

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  • DOI: https://doi.org/10.1007/BFb0052370

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  • Print ISBN: 978-3-540-64301-2

  • Online ISBN: 978-3-540-69721-3

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