On the proof complexity of deep inference

Authors:
Paola Bruscoli;Alessio Guglielmi
Affiliations:
University of Bath, Bath, UK;University of Bath, Bath, UK
Venue:
ACM Transactions on Computational Logic (TOCL)
Year:
2009

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Abstract

We obtain two results about the proof complexity of deep inference: (1) Deep-inference proof systems are as powerful as Frege ones, even when both are extended with the Tseitin extension rule or with the substitution rule; (2) there are analytic deep-inference proof systems that exhibit an exponential speedup over analytic Gentzen proof systems that they polynomially simulate.