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Linear lower bounds and simulations in frege systems with substitutions

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Computer Science Logic (CSL 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1414))

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Abstract

We investigate the complexity of proofs in Frege (F), Substitution Frege (sF) and Renaming Frege (rF) systems. Starting from a recent work of Urquhart and using Kolmogorov Complexity we give a more general framework to obtain superlogarithmic lower bounds for the number of lines in both tree-like and dag-like sF. We show the previous known lower bound, extend it to the tree-like case and, for another class of tautologies, we give new lower bounds that in the dag-like case slightly improve the previous one. Also we show optimality of Urquhart's lower bounds giving optimal proofs. Finally we give the following two simulation results: (1) tree-like sF p-simulates dag-like sF; (2) Tree-like F p-simulates tree-like rF.

Research partly supported by NSF grant number CCR-9403447.

Supported by European Community grant under the project Training and Mobility of Researchers.

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Authors and Affiliations

  1. Dept. de Llenguatges i Sistemes Informatics, Universitat Politecnica de Catalunya, Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Maria Luisa Bonet & Nicola Galesi

Authors
  1. Maria Luisa Bonet
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  2. Nicola Galesi
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Mogens Nielsen Wolfgang Thomas

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© 1998 Springer-Verlag Berlin Heidelberg

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Bonet, M.L., Galesi, N. (1998). Linear lower bounds and simulations in frege systems with substitutions. In: Nielsen, M., Thomas, W. (eds) Computer Science Logic. CSL 1997. Lecture Notes in Computer Science, vol 1414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028010

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  • DOI: https://doi.org/10.1007/BFb0028010

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64570-2

  • Online ISBN: 978-3-540-69353-6

  • eBook Packages: Springer Book Archive

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