Tautologies from pseudo-random generators

Bulletin of Symbolic Logic

Volumn 7, Issue 2, 2001, Pages 197-212

  Krajíček, Jan ^a,b  

^a MATHEMATICAL INSTITUTE   (Czech Republic)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035534383     PISSN: 10798986     EISSN: None     Source Type: Journal    
DOI: 10.2307/2687774     Document Type: Article

References (33)

1. th annual symposium on foundation of computer science, 1988, pp. 346-355.
2. M. ALEKHNOVICH, E. BEN-SASSON, A. A. RAZBOROV, and A. WIGDERSON, Pseudorandom generators in propositional proof complexity, preprint, March 2000.
3. S. R. Buss, Bounded arithmetic, Bibliopolis, Naples, 1986, Revision of 1985 Princeton University Ph.D. thesis.
4. A COBHAM, The intrinsic computational difficulty of functions, Proceedings of logic, methodology and philosophy of science (Y. Bar-Hillel, editor), North-Holland, 1965, pp. 24-30.
5. rd annual ACM symposium on theory of computing, ACM Press, 1971, pp. 151-158.
6. th annual ACM symposium on theory of computing, ACM Press, 1975, pp. 83-97.
7. S. A. COOK and A. R. RECKHOW, The relative efficiency of propositional proof systems, The Journal of Symbolic Logic, vol. 44 (1979), no. 1, pp. 36-50.
8. M. DOWD, Propositional representations of arithmetic proofs, Ph.D. thesis, University of Toronto, 1979.
9. A. HAKEN, The intractability of resolution, Theoretical Computer Science, vol. 39 (1985), pp. 297-308.
10. th annual ACM symposium on theory of computing, 1997, pp. 220-229.
11. J. KRAJÍČEK, On the weak pigeonhole principle, to appear in FUNDAMENTA MATHEMATICAE (preprint on web August 9 '99).
12. -, Speed-up for propositional Frege systems via generalizations of proofs, Commentationes Mathematicae Universitatis Carolinae, vol. 30 (1989), no. 1, pp. 137-140.
13. -, Lower bounds to the size of constant-depth propositional proofs, The Journal of Symbolic Logic, vol. 59 (1994), no. 1, pp. 73-86.
14. -, Bounded arithmetic, propositional logic, and complexity theory, Encyclopedia of mathematics and its applications, vol. 60, Cambridge University Press, 1995.
15. -, On Frege and extended Frege proof systems, "Feasible mathematics II" (P. Clote and J. Remmel, editors), Birkhauser, 1995, pp. 284-319.
16. -, Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic, The Journal of Symbolic Logic, vol. 62 (1997), no. 2, pp. 457-486.
17. J. KRAJÍČEK and P. PUDLÁK, Propositional proof systems, the consistency of first order theories and the complexity of computations, The Journal of Symbolic Logic, vol. 54 (1989), no. 3, pp. 1063-1079.
18. -, Propositional provability in models of weak arithmetic, Computer science logic, October 1989 (Kaiserlautern) (E. Boerger, H. Kleine-Bunning, and M. M. Richter, editors), Lecture Notes in Computer Science, vol. 440, Springer-Verlag, 1990, pp. 193-210.
19. -, Quantified propositional calculi and fragments of hounded arithmetic, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 36 (1990), pp. 29-46.
20. 2 and EF, Information and Computation, vol. 140 (1998), no. 1, pp. 82-94.
21. J. KRAJÍČEK, P. PUDLÁK, and J. SGALL, Interactive computations of optimal solutions, Mathematical foundations of computer science (B. Rovan, editor), Lecture Notes in Computer Science, vol. 452, Springer-Verlag, B. Bystrica, August 1990, pp. 48-60.
22. J. KRAJÍČEK, P. PUDLÁK, and G. TAKEUTI, Bounded arithmetic and the polynomial hierarchy, Annals of Pure and Applied Logic, vol. 52 (1991), pp. 143-153.
23. A. MACIEL, T. PITASSI, and A. WOODS, A new proof of the weak pigeonhole principle, preprint, 1999.
24. J. PARIS and A. J. WILKIE, Counting problems in bounded arithmetic, Methods in mathematical logic, Lecture Notes in Mathematics, vol. 1130, Springer-Verlag, 1985, pp. 317-340.
25. J. B. PARIS, A. J. WILKIE, and A. R. WOODS, Probability of the pigeonhole principle and the existence of infinitely many primes, The Journal of Symbolic Logic, vol. 53 (1988), pp. 1235-1244.
26. P. PUDLÁK, Some relations between subsystems of arithmetic and the complexity of computations, Logic from computer science (Y. N. Moschovakis, editor), Mathematical Sciences Research Institute Publication, vol. 21, Springer-Verlag, 1992, proceedings of a workshop held November 13-17, 1989 in Berkeley, pp. 499-519.
27. -, The lengths of proofs, Handbook of proof theory (S. Buss, editor), Elsevier, 1997.
28. A. A. RAZBOROV, Bounded arithmetic and lower bounds in Boolean complexity, Feasible mathematics (P. Clote and J. Remmel, editors), Progress in Computer Science and Applied Logic, vol. 13, Birkhauser, 1995, pp. 344-386.
29. -, Unprovability of lower bounds on the circuit size in certain fragments of bounded arithmetic, Rossiǐskaya Akademiya Nauk. Izvestiya. Seriya Matematicheskaya, vol. 59 (1995), no. 1, pp. 201-224.
30. A. A. RAZBOROV and S. RUDICH, Natural proofs, Journal of Computer and System Sciences, vol. 55 (1997), no. 1, pp. 24-35.
31. G. C. TSEITIN, On the complexity of derivations in propositional calculus, Studies in mathematics and mathematical logic, part II (A. O. Slisenko, editor), 1968, pp. 115-125.
32. A. URQUHART, The complexity of propositional proofs, this BULLETIN, vol. 1 (1995), no. 4, pp. 425-467.
33. rd annual symposium on foundation of computer science, 1982, pp. 92-99.