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The cost of a cycle is a square

Published online by Cambridge University Press:  12 March 2014

A. Carbone
A. Carbone*
Affiliation:
Mathématiques/Informatique, Université de Paris XII, 61 Avenue Du Général De Gaulle, 94010 Créteil Cedex, France, E-mail: carbone@ihes.fr
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Abstract

The logical flow graphs of sequent calculus proofs might contain oriented cycles. For the predicate calculus the elimination of cycles might be non-elementary and this was shown in [Car96]. For the propositional calculus, we prove that if a proof of k lines contains n cycles then there exists an acyclic proof with (kn+1) lines. In particular, there is a polynomial time algorithm which eliminates cycles from a proof. These results are motivated by the search for general methods on proving lower bounds on proof size and by the design of more efficient heuristic algorithms for proof search.

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Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 1 , March 2002 , pp. 35 - 60
Copyright
Copyright © Association for Symbolic Logic 2002

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