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Paper:

TR21-176 | 30th November 2021 04:19

A super-polynomial separation between resolution and cut-free sequent calculus

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TR21-176
Authors: Theodoros Papamakarios
Publication: 8th December 2021 22:55
Downloads: 116
Keywords: 


Abstract:

We show a quadratic separation between resolution and cut-free sequent calculus width. We use this gap to get, for the first time, first, a super-polynomial separation between resolution and cut-free sequent calculus for refuting CNF formulas, and secondly, a quadratic separation between resolution width and monomial space in polynomial calculus with resolution. Our super-polynomial separation between resolution and cut-free sequent calculus only applies when clauses are seen as disjunctions of unbounded arity; our examples have linear size cut-free sequent calculus proofs writing, in a particular way, their clauses using binary disjunctions. Interestingly, this shows that the complexity of sequent calculus depends on how disjunctions are represented.



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