Abstract
We prove lower bounds for a proof system having exponential speed-up over both polynomial calculus and constant-depth Frege systems in DeMorgan language.
Partially supported by cooperative research grant INT-9600919/ME-103 from the NSF (USA) and the MŠMT (Czech republic) and by the grant #A1019602 of the Academy of Sciences of the Czech Republic.
On leave from the Mathematical Institute of the Academy of Sciences at Prague.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Beame, P., Impagliazzo, R., Krajíček, J., Pitassi, T., Pudlák, P.: Lower bounds on Hilbert's Nullstellensatz and propositional proofs. Proceedings of the London Mathematical Society 73(3) (1996) 1–26
Beame, P., Riis, S.: More on the relative strength of counting principles. (submitted)
Buss, S., Impagliazzo, R., Krajiček, J., Pudlák, P., Razborov, A. A., Sgall, J.: Proof complexity in algebraic systems and bounded depth Frege systems with modular counting. Computational Complexity (to appear)
Clegg, M, Edmonds, J., Impagliazzo, R.: Using the Groebner basis algorithm to find proofs of unsatisfiability. In: Proceedings of the 28th ACM Symposium on Theory of Computing, ACM (1996) 174–183
Krajĩcek, J.: Bounded arithmetic, propositional logic, and complexity theory. Encyclopedia of Mathematics and Its Applications, Vol. 60 Cambridge University Press (1995)
Krajićek, J.: A fundamental problem of mathematical logic. Annals of the Kurt Gödel Society, Springer-Verlag, Collegium Logicum, 2 (1995) 56–64
Krajićek, J.: On methods for proving lower bounds in propositional logic. In: Logic and Scientific Methods Eds. M. L. Dalla Chiara et al., (Vol. 1 of Proc. of the Tenth International Congress of Logic, Methodology and Philosophy of Science, Florence (August 19–25, 1995)), Synthese Library, 259 Kluwer Academic Publ., Dordrecht (1997) 69–83
Krajićek, J.: On the degree of ideal membership proofs from uniform families of polynomials over a finite field. (in preparation)
Krajićek, J.,Pudlák, P., Woods, A.: Exponential lower bound to the size of bounded depth Frege proofs of the pigeonhole principle. Random Structures and Algorithms 7(1) (1995) 15–39
Pitassi, T., Beame, P., and Impagliazzo, R.: Exponential lower bounds for the pigeonhole principle. Computational Complexity 3(2) (1993) 97–140
Pudlák, P.: The lengths of proofs. In: Handbook of Proof Theory, Ed. S. Buss, (to appear)
Razborov, A. A.: Lower bounds for propositional proofs and independence results in bounded arithmetic. In: Proc. of the 23rd ICALP, F.Meyer auf der Heide and B. Monien eds., LN in Computer Science, 1099, Springer-Verlag, (1996) 48–62
Razborov, A. A.: Lower bounds for the polynomial calculus. (submitted)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Krajiček, J. (1997). Lower bounds for a proof system with an exponential speed-up over constant-depth Frege systems and over polynomial calculus. In: Prívara, I., Ružička, P. (eds) Mathematical Foundations of Computer Science 1997. MFCS 1997. Lecture Notes in Computer Science, vol 1295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0029951
Download citation
DOI: https://doi.org/10.1007/BFb0029951
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63437-9
Online ISBN: 978-3-540-69547-9
eBook Packages: Springer Book Archive