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International Workshop on Computer Science Logic

CSL 1994: Computer Science Logic pp 190–204Cite as

Monadic logical definability of NP-complete problems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 933))

Abstract

It is well known that monadic second-order logic with linear order captures exactly regular languages. On the other hand, if addition is allowed, then J.F.Lynch has proved that existential monadic secondorder logic captures at least all the languages in NTIME(n), and then expresses some NP-complete languages (e.g. knapsack problem).

It seems that most combinatorial NP-complete problems (e.g. traveling salesman, colorability of a graph) do not belong to NTIME(n). But it has been proved that they do belong to NLIN (the similar class for RAM's). In the present paper, we prove that existential monadic second-order logic with addition captures the class NLIN, so enlarging considerably the set of natural problems expressible in this logic. Moreover, we also prove that this logic still captures NLIN even if first-order part of the second-order formulas is required to be ∀*∃*, so improving the recent similar result of J.F.Lynch about NTIME(n).

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Authors and Affiliations

  1. LAIAC, Université de Caen, France

    Etienne Grandjean & Frédéric Olive

Authors
  1. Etienne Grandjean
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  2. Frédéric Olive
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Editor information

Leszek Pacholski Jerzy Tiuryn

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© 1995 Springer-Verlag Berlin Heidelberg

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Grandjean, E., Olive, F. (1995). Monadic logical definability of NP-complete problems. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022256

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  • DOI: https://doi.org/10.1007/BFb0022256

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60017-6

  • Online ISBN: 978-3-540-49404-1

  • eBook Packages: Springer Book Archive

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