A Quasipolynomial Cut-Elimination Procedure in Deep Inference via Atomic Flows and Threshold Formulae
Abstract
Jeřábek showed in 2008 that cuts in propositional-logic deep-inference proofs can be eliminated in quasipolynomial time. The proof is an indirect one relying on a result of Atserias, Galesi and Pudlák about monotone sequent calculus and a correspondence between this system and cut-free deep-inference proofs. In this paper we give a direct proof of Jeřábek's result: we give a quasipolynomial-time cut-elimination procedure in propositional-logic deep inference. The main new ingredient is the use of a computational trace of deep-inference proofs called atomic flows, which are both very simple (they trace only structural rules and forget logical rules) and strong enough to faithfully represent the cut-elimination procedure.
- Publication:
-
Lecture Notes in Computer Science
- Pub Date:
- 2010
- DOI:
- 10.1007/978-3-642-17511-4_9
- arXiv:
- arXiv:0903.5392
- Bibcode:
- 2010LNCS.6355..136B
- Keywords:
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- Computer Science - Computational Complexity;
- Computer Science - Logic in Computer Science;
- F.4.1;
- F.2.2
- E-Print:
- Accepted by Logical Methods in Computer Science