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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.

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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