Linear lower bounds and simulations in frege systems with substitutions

  • Maria Luisa Bonet
  • Nicola Galesi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1414)


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.


Proof System Binary String Propositional Variable Kolmogorov Complexity Random String 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Maria Luisa Bonet
    • 1
  • Nicola Galesi
    • 1
  1. 1.Dept. de Llenguatges i Sistemes InformaticsUniversitat Politecnica de CatalunyaBarcelonaSpain

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