Polynomial-time algorithms from ineffective proofs

Proceedings - Symposium on Logic in Computer Science

Volumn , Issue , 2003, Pages 128-137

  Oliva, Paulo ^a  

^a AARHUS UNIVERSITY   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; MATHEMATICAL MODELS; THEOREM PROVING; COMPUTER SCIENCE; DIGITAL ARITHMETIC; MATHEMATICAL TECHNIQUES; POLYNOMIAL APPROXIMATION; POLYNOMIALS;

POLYNOMIAL-TIME ALGORITHMS;

POLYNOMIALS; ALGORITHMS;

EQUATIONS; FUNCTIONAL INTERPRETATIONS; LOGIC; POLYNOMIAL-TIME; POLYNOMIAL-TIME ALGORITHMS; RECURSIONS;

EID: 0041466272     PISSN: 10436871     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (21)

1. J. Avigad and S. Feferman. Gödel's functional ("Dialectica") interpretation. In S. R. Buss, editor, Handbook of proof theory, volume 137 of Studies in Logic and the Foundations of Mathematics, pages 337-405. Elsevier, North-Holland, Amsterdam, 1998.
2. S. R. Buss. Bounded arithmetic, PhD thesis, Princeton University, Princeton, New Jersey, 1985.
3. S. R. Buss. The polynomial hierarchy and intuitionistic bounded arithmetic. In G. Goos and J. Hartmanis, editors, Structure in Complexity Theory, volume 223 of Lecture Notes in Computer Science, pages 77-103, Springer-Verlag, 1986.
4. S. Cook. Feasibly constructive proofs and the prepositional calculus. In Proc. 7th A.C.M. Symposium on the Theory of Computation, pages 83-97, 1975.
5. S. Cook and A. Urquhart. Functional interpretations of feasibly constructive arithmetic. Annals of Pure and Applied Logic, 63:103-200, 1993.
6. F. Ferreira. A feasible theory for analysis. Journal of Symbolic Logic, 59(3):1001-1011, 1994.
7. F. Ferreira and A. Fernandas. Basic applications of weak König's lemma in feasible analysis. Submitted.
8. H. Friedman. Systems of second order arithmetic with restricted induction, I, II (abstracts). Journal of Symbolic Logic, 41:557-559, 1976.
9. W. A. Howard. Ordinal analysis of simple cases of bar recursion. Journal of Symbolic Logic, 46(1):17-30, 1981.
10. B. Kapron and S. Cook. A new characterization of type-2 feasibility. SIAM Journal Computing, 25(1):117-132, 96.
11. B. Kauffmann. Application of Proof Theory to Computational Complexity Theory: Comparison of Different Methods. PhD thesis, Carnegie Mellon University, Department of Philosophy, 2001.
12. U. Kohlenbach. Effective bounds from ineffective proofs in analysis: an application of functional interpretation and majorization. Journal of Symbolic Logic, 57:1239-1273, 1992.
13. U. Kohlenbach. Mathematically strong subsystems of analysis with low rate of growth of provably recursive functionals. Archive for Mathematical Logic, 36:31-71, 1996.
14. U. Kohlenbach. On the no-counterexample interpretation. Journal of Symbolic Logic, 64:1491-1511, 1999.
15. 1-approximation. Annals of Pure and Applied Logic, 121:1-38, 2003.
16. H. Luckhardt. Extensional Gödel functional interpretation - a consistency proof of classical analysis. In Lecture Notes in Mathematics, volume 306. Springer Verlag, 1973.
17. B. Scarpellini. A model for bar recursion of higher types. Compositio Mathematica, 23:123-153, 1971.
18. W. Sieg. Hubert's program sixty years later. Journal of Symbolic Logic, 53:338-348, 1988.
19. W. Sieg. Herbrand analyses. Archive for Mathematical Logic, 30:409-441, 1991.
20. S. G. Simpson. Subsystems of Second Order Arithmetic. Perspectives in Mathematical Logic. Springer-Verlag, 1999.
21. C. Spector. Provably recursive functionals of analysis: a consistency proof of analysis by an extension of principles in current intuitionistic mathematics. In F. D. E. Dekker, editor, Recursive Function Theory: Proc. Symposia in Pure Mathematics, volume 5, pages 1-27. American Mathematical Society, Providence, Rhode Island, 1962.