On characterizations of the basic feasible functionals, Part I

Journal of Functional Programming

Volumn 11, Issue 1, 2001, Pages 117-153

  Irwin, Robert J ^a   Royer, James S ^a   Kapron, Bruce M ^b  

^a Syracuse University   (United States)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035630598     PISSN: 09567968     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956796800003841     Document Type: Article

References (49)

1. Asperti, A. (1998) Light affine logic. Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science.
2. Bellantoni, S. (1992) Predicative recursion and computational complexity. PhD thesis, University of Toronto. (University of Toronto Computer Science Department, Technical Report 264/92.)
3. Bellantoni, S. and Cook, S. (1992) A new recursion-theoretic characterization of the polytime functions. Computational Complexity, 2, 97-110.
4. Bellantoni, S., Niggl, K.-H. and Schwichtenberg, H. (2000) Characterising polytime through higher type recursion. Annals of Pure and Applied Logic. To appear.
5. Buss, S. (1986) The polynomial hierarchy and intuitionistic bounded arithmetic. In: Selman, A. (ed.), Structure in Complexity Theory: Lecture Notes in Computer Science 223, pp. 77-103. Springer-Verlag.
6. Cobham, A. (1965) The intrinsic computational difficulty of functions. In: Bar Hillel, Y. (ed.), Proceedings of the International Conference on Logic, Methodology and Philosophy, pp. 24-30. North-Holland.
7. Constable, R. (1973) Type two computational complexity. Proceedings of the Fifth Annual ACM Symposium on the Theory of Computing, pp. 108-121.
8. Cook, S. (1971) The complexity of theorem proving procedures. Proceedings of the Third Annual ACM Symposium on the Theory of Computing, pp. 151-158.
9. Cook, S. (1991) Computability and complexity of higher type functions. In: Moschovakis, Y.N. (ed), Logic from Computer Science, pp. 51-72. Springer-Verlag.
10. Cook, S. and Kapron, B. (1989) Characterizations of the basic feasible functions of finite type. Proceedings of the 30th Annual IEEE Symposium on the Foundations of Computer Science, pp. 154-159.
11. Cook, S. and Kapron, B. (1990) Characterizations of the basic feasible functions of finite type. In: Buss, S. and Scott, P. (eds.), Feasible Mathematics: A Mathematical Sciences Institute Workshop, pp. 71-95. Birkhäuser.
12. Cook, S. and Urquhart, A. (1989) Functional interpretations of feasibly constructive arithmetic. Proceedings of the 21st Annual ACM Symposium on the Theory of Computing, pp. 107-112.
13. Cook, S. and Urquhart, A. (1993) Functional interpretations of feasibly constructive arithmetic. Annals of Pure and Applied Logic, 63, 103-200.
14. Gandy, R. and Hyland, J. (1977) Computable and recursively countable functions of higher type. Logic Colloquium 76, pp. 407-438. North-Holland.
15. Girard, J.-Y. (1998) Light linear logic. Information and Computation, 143, 175-204.
16. Girard, J.-Y., Scedrov, A. and Scott, P.J. (1992) Bounded linear logic: A modular approach to polynomial time computability. Theoretical Computer Science, 97, 1-66.
17. Gödel, K. (1958) Über eine bisher noch nicht benützte Erweiterung des finiten. Dialectica, 12, 280-287.
18. Gödel, K. (1990) On a hitherto unutilized extension of the finitary standpoint. In: Feferman, S., Dawson, J., Kleene, S., Moore, G., Solovay, R., & van Heijenoort, J. (eds.), Kurt Gödel: Collected Works, Volume II, pp. 241-251. Oxford University Press.
19. Hubert, D. (1925) Über das unendliche. Mathematische annalen, 95, 161-190.
20. Hubert, D. (1967) On the infinite. In: van Heijenoort, J. (ed.), From Frege to Gödel: A source book in mathematical logic, 1879-1931, pp. 367-392. Harvard University Press.
21. Hofmann, M. (1997) An application of category-theoretic semantics to the characterisation of complexity classes using higher-order function algebras. Bulletin of Symbolic Logic, 3, 469-486.
22. Hofmann, M. (1999a) Linear types and non-size-increasing polynomial time computation. Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science.
23. Hofmann, M. (1999b) Type systems for polynomial-time computation. Habilitation thesis, Darmstadt. (University of Edinburgh LFCS Technical Report ECS-LFCS-99-406.)
24. Jones, N. (1997) Computability and Complexity from a Programming Perspective. MIT Press.
25. Kapron, B. and Cook, S. (1991) A new characterization of Mehlhorn's polynomial time functionals. Proceedings of the 32nd Annual IEEE Symposium Foundations of Computer Science, pp. 342-347.
26. Kapron, B. and Cook, S. (1996) A new characterization of type 2 feasibility. SIAM Journal on Computing, 25, 117-132.
27. Kreisel, G., Lacombe, D. and Shoenfield, J. (1957) Partial recursive functionals and effective operations. In: Heyting, A. (ed.), Constructivity in Mathematics: Proceedings of the Colloquium held at Amsterdam, pp. 195-207. North-Holland.
28. Leivant, D. (1991) A foundational delineation of computational feasibility. Proceedings of the Sixth IEEE Conference on Logic in Computer Science, pp. 2-11.
29. Leivant, D. (1994a) A foundational delineation of poly-time. Information and Computation, 110, 391-120.
30. Leivant, D. (1994b) Predicative recurrence in finite types. In: Nerode, A. and Matiyasevich, Yu. (eds.), Logical Foundations of Computer Science: Third International Symposium, lfcs '94: Lecture Notes in Computer Science 813, pp. 227-239. Springer-Verlag.
31. Leivant, D. (1995) Ramified recurrence and computational complexity I: Word recurrence and poly-time. In: Clote, P. and Remmel, J. (eds.), Feasible Mathematics II, pp. 320-343. Birkhäuser.
32. Mehlhorn, K. (1974) Polynomial and abstract subrecursive classes. Proceedings of the Sixth Annual ACM Symposuium on the Theory of Computing, pp. 96-109.
33. Mehlhorn, K. (1976) Polynomial and abstract subrecursive classes. J. Computer and System Science, 12, 147-178.
34. Nelson, E. (1986) Predicative Arithmetic. Princeton University Press.
35. Otto, J. (1995) Complexity doctrines. PhD thesis, McGill University.
36. Pezzoli, E. (1998) On the computational complexity of type two functionals. In: van Dalen, D. and Bezem, M. (eds.), Proceedings of the Conference for Computer Science Logic '97: Lecture Notes in Computer Science 1414, pp. 373-388. Springer-Verlag.
37. Rogers, H. (1967) Theory of Recursive Functions and Effective Computability. McGraw-Hill. MIT Press (reprinted 1987).
38. Royer, J. (1997) Semantics versus syntax versus computations: Machine models for type-2 polynomial-time bounded functionals. J. Computer and System Science, 54, 424-436.
39. Royer, J. and Case, J. (1994) Subrecursive Programming Systems: Complexity & succinctness. Birkhäuser.
40. Russell, B. (1903) The Principles of Mathematics, Vol. I. Cambridge University Press.
41. Russell, B. (1908) Mathematical logic as based on the theory of types. Am. J. Mathematics, 30, 222-262.
42. Russell, B. (1967) Mathematical logic as based on the theory of types. In: van Heijenoort, J. (ed), From Frege to Gödel: A source book in mathematical logic, 1879-1931. Harvard University Press.
43. Seth, A. (1992) There is no recursive axiomatization for feasible functionals of type 2. Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science, pp. 286-295.
44. Seth, A. (1993) Some desirable conditions for feasible functions of type 2. Proceedings of the Eighth Annual IEEE Symposium on Logic in Computer Science, pp. 320-331.
45. Seth, A. (1994) Complexity theory of higher type functionals. PhD thesis, University of Bombay.
46. Seth, A. (1995) Turing machine characterizations of feasible functionals of all finite types. In: Clote, P. and Remmel, J. (eds.), Feasible Mathematics II, pp. 407-128. Birkhauser.
47. Townsend, M. (1990) Complexity for type-2 relations. Notre Dame J. Formal Logic, 31, 241-262.
48. Turing, A. (1936) On computable numbers, with an application to the entscheidungsproblem. Proc. London Mathematical Society, 42, 230-265.
49. Young, P. (1990) Juris Hartmanis: Fundamental contributions to isomorphism problems. In: Selman, A. (ed.), Complexity Theory Retrospective, pp. 28-58. Springer-Verlag.