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Hardness assumptions in the foundations of theoretical computer science

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References

  1. Alekhnovich, M., Ben-Sasson, E., Razborov, A.A., Wigderson, A.: Pseudorandom generators in propositional proof complexity, Ext. abstract. In: Proc. of the 41st Annual Symp. on Foundation of Computer Science, 2000, pp.43–53

  2. Cook, S.A.: The complexity of theorem proving procedures. In: Proc. 3rd Annual ACM Symp. on Theory of Computing, ACM Press, 1971, pp. 151–158

  3. Cook, S. A.: Feasibly constructive proofs and the propositional calculus. In: Proc. 7th Annual ACM Symp. on Theory of Computing, ACM Press, 1975, pp. 83–97

  4. Cook, S. A.: The P versus NP problem, at: http://www.claymath.org/ prizeproblems/pvsnp.htm

  5. Cook, S.A., Reckhow, A.R.: The relative efficiency of propositional proof systems, J. Symbolic Logic, 44 (1), 1979, pp.36–50

    Google Scholar 

  6. Goldreich, O.: Foundations of Cryptography, Vol.1, Cambridge University Press, (2001)

  7. Hastad, J., Impagliazzo, R., Levin, L., Luby, M.: A Pseudorandom Generator from any one-way function, SIAM Journal on Computing, vol. 28, 1999, pp 1364–1396

  8. Impagliazzo, R., Wigderson, A.: P = BPP unless E has sub-exponential circuits: derandomizing the XOR lemma. In: Proc. of the 29th Annual ACM Symposium on Theory of Computing, 1997, pp. 220–229

  9. Krajíček, J.: Bounded arithmetic, propositional logic, and complexity theory, Encyclopedia of Mathematics and Its Applications, vol. 60, Cambridge University Press, (1995).

  10. Krajíček, J.: On the weak pigeonhole principle, Fundamenta Mathematicae, vol. 170 (1–3), 2001, pp.123–140

  11. Krajíček, J.: Tautologies from pseudo-random generators, Bulletin of Symbolic Logic, 7 (2), (2001), pp.197–212

  12. Krajíček, J.: Dual weak pigeonhole principle, pseudo-surjective functions, and provability of circuit lower bounds, J. of Symbolic Logic, 69 (1), 2004, pp. 265–286

    Google Scholar 

  13. Krajíček, J., Pudlák, P.: Propositional proof systems, the consistency of first order theories and the complexity of computations, J. Symbolic Logic, 54 (3), 1989, pp. 1063–1079

    Google Scholar 

  14. Levin, L.: Universal Search Problems (in Russian), Problems of Information Transmission, 9 (3), 1973, pp. 265–266

  15. Razborov, A.A.: Resolution lower bounds for perfect matching principles, In: Proc. of the 17th IEEE Conf. on Computational Complexity, 2002, pp. 29–38

  16. Razborov, A.A.: Pseudorandom generators hard for k-DNF resolution and polynomial calculus resolution, preprint, December’02

  17. Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring, In: Proc. 35nd Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, 1994, pp. 124–134

  18. Sipser, M.: The history and status of the P versus NP question, In: Proceedings of the 24th Annual ACM Symposium on Theory of Computing, ACM Press, 1992, pp. 603–618

  19. Smale, S.: Mathematical Problems for the Next Century, Math. Intelligencer, 20 (2), 1998, pp. 7–15

    Google Scholar 

  20. Yao, A.C.-C.: Classical Physics and the Church-Turing Thesis, ECCC:http://www.eccc.uni-trier.de/eccc-local/Lists/TR-2002.html TR02-062.

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Correspondence to Jan Krajíček.

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Partially supported by grant # A 101 99 01 of the Academy of Sciences of the Czech Republic and by project LN00A056 of The Ministry of Education of the Czech Republic. A part of this paper was written while visiting the Mathematical Institute in Oxford, supported by the EPSRC.

Also member of the Institute for Theoretical Computer Science of the Charles University.

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Krajíček, J. Hardness assumptions in the foundations of theoretical computer science. Arch. Math. Logic 44, 667–675 (2005). https://doi.org/10.1007/s00153-005-0279-x

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