Abstract
A new approach to defining complexity of propositional formulas and proofs is suggested. Instead of measuring the size of these syntactical structures in the propositional language, the article suggests to define the complexity by the size of external descriptions of such constructions. The main result is a lower bound on proof complexity with respect to this new definition of complexity.
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References
Cook S.A., Reckhow R.A.: The relative efficiency of propositional proof systems. J. Symbolic Logic 44(1), 36–50 (1979)
Cook W., Coullard C.R., Turán Gy.: On the complexity of cutting-plane proofs. Discrete Appl. Math. 18(1), 25–38 (1987)
Haken, A.: The intractability of resolution. Theor. Comput. Sci. 39(2–3), 297–308 (1985)
Krajíček J.: Diagonalization in proof complexity. Fund. Math. 182(2), 181–192 (2004)
Krajíček J.: Implicit proofs. J. Symbolic Logic 69(2), 387–397 (2004)
Krajíček J.: Structured pigeonhole principle, search problems and hard tautologies. J. Symbolic Logic 70(2), 619–630 (2005)
Krajíček J., Pudlák P., Woods A.: An exponential lower bound to the size of bounded depth Frege proofs of the pigeonhole principle. Random Struct. Algorithms 7(1), 15–39 (1995)
Parikh R.J.: Some results on the lengths of proofs. Trans. Am. Math. Soc. 177, 29–36 (1973)
Pitassi T., Beame P., Impagliazzo R.: Exponential lower bounds for the pigeonhole principle. Comput. Complexity 3(2), 97–140 (1993)
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Naumov, P. On meta complexity of propositional formulas and propositional proofs. Arch. Math. Logic 47, 35–52 (2008). https://doi.org/10.1007/s00153-008-0068-4
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DOI: https://doi.org/10.1007/s00153-008-0068-4