Abstract
We consider the fragment of deep inference free of compression mechanisms and compare its proof complexity to other systems, utilising ‘atomic flows’ to examine size of proofs. Results include a simulation of Resolution and dag-like cut-free Gentzen, as well as a separation from bounded-depth Frege.
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References
Brünnler, K., Tiu, A.F.: A local system for classical logic (2001); preprint (WV-01-02) (2001)
Bruscoli, P., Guglielmi, A.: On the proof complexity of deep inference. ACM Transactions on Computational Logic 10(2), article 14, 1–34 (2009)
Bruscoli, P., Guglielmi, A., Gundersen, T., Parigot, M.: Quasipolynomial normalisation in deep inference via atomic flows and threshold formulae (2009) (submitted)
Buss, S.R.: Polynomial size proofs of the propositional pigeonhole principle. Journal of Symbolic Logic 52(4), 916–927 (1987)
Clote, P., Kranakis, E.: Boolean Functions and Computation Models. Springer (2002)
D’Agostino, M.: Are tableaux an improvement on truth-tables? Journal of Logic, Language and Information 1, 235–252 (1992)
Das, A.: On the Proof Complexity of Cut-Free Bounded Deep Inference. In: Brünnler, K., Metcalfe, G. (eds.) TABLEAUX 2011. LNCS, vol. 6793, pp. 134–148. Springer, Heidelberg (2011)
Das, A.: Complexity of deep inference via atomic flows (2012)(preprint)
Guglielmi, A.: Resolution in the calculus of structures (2003) (preprint)
Guglielmi, A., Gundersen, T.: Normalisation control in deep inference via atomic flows II (2008) (preprint)
Gundersen, T.: A General View of Normalisation Through Atomic Flows. Ph.D. thesis, University of Bath (2009)
Jeřábek, E.: Proof complexity of the cut-free calculus of structures. Journal of Logic and Computation 19(2), 323–339 (2009)
Krajíček, J.: On the weak pigeonhole principle (2001)
Krajíček, J., Pudlák, P., Woods, A.: An exponential lower bound to the size of bounded depth frege proofs of the pigeonhole principle. Random Structures & Algorithms 7(1), 15–39 (1995)
Pitassi, T., Beame, P., Impagliazzo, R.: Exponential lower bounds for the pigeonhole principle. Computational Complexity 3, 97–140 (1993)
Troelstra, A., Schwichtenberg, H.: Basic Proof Theory. Cambridge Tracts in Theoretical Computer Science, vol. 43. Cambridge University Press (1996)
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Das, A. (2012). Complexity of Deep Inference via Atomic Flows. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_15
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DOI: https://doi.org/10.1007/978-3-642-30870-3_15
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