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Archive for Mathematical Logic

, Volume 53, Issue 7–8, pp 949–967 | Cite as

On the complexity of the closed fragment of Japaridze’s provability logic

  • Fedor Pakhomov
Article

Abstract

We consider the well-known provability logic GLP. We prove that the GLP-provability problem for polymodal formulas without variables is PSPACE-complete. For a number n, let \({L^{n}_0}\) denote the class of all polymodal variable-free formulas without modalities \({\langle n \rangle,\langle n+1\rangle,...}\). We show that, for every number n, the GLP-provability problem for formulas from \({L^{n}_0}\) is in PTIME.

Keywords

Provability logic Computational complexity Closed fragment 

Mathematics Subject Classification

03F45 03D15 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteMoscowRussia

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