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Incorporating generalized quantifiers and the least fixed point operator

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Computer Science Logic (CSL 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 832))

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Abstract

We extend first-order logic with successor using the least fixed point operator and the Hamiltonian path generalized quantifier simultaneously, and show that the complexity class captured is PNP: we also obtain a normal form for this logic. We consider the incorporation of the least fixed point operator into other logics capturing NP and see that this may present difficulties in general. We apply our results to obtain, amongst other results, a new complete problem for PNP involving the evaluation of logically defined functions.

Supported by SERC Grant GR/H 81108.

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Authors and Affiliations

  1. Department of Computer Science, University College of Swansea, SA2 8PP, Swansea, UK

    Iain A. Stewart

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  1. Iain A. Stewart
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Editor information

Egon Börger Yuri Gurevich Karl Meinke

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© 1994 Springer-Verlag Berlin Heidelberg

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Stewart, I.A. (1994). Incorporating generalized quantifiers and the least fixed point operator. In: Börger, E., Gurevich, Y., Meinke, K. (eds) Computer Science Logic. CSL 1993. Lecture Notes in Computer Science, vol 832. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0049340

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  • DOI: https://doi.org/10.1007/BFb0049340

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58277-9

  • Online ISBN: 978-3-540-48599-5

  • eBook Packages: Springer Book Archive

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