Implicit computational complexity for higher type functionals (Extended abstract)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2471, Issue , 2002, Pages 367-381

  Leivant, Daniel ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTABLE FUNCTIONS; COMPUTATIONAL FEASIBILITY; EXTENDED ABSTRACTS; FEASIBLE FUNCTIONALS; IMPLICIT COMPUTATIONAL COMPLEXITY; POSITIVE FORMULA; SECOND-ORDER LOGIC; TYPE ARGUMENTS;

COMPUTER CIRCUITS;

EID: 23044533230     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45793-3_25     Document Type: Conference Paper

References (27)

1. [1] Samuel Buss. Bounded Arithmetic. Bibliopolis, Naples, 1986.
2. Samuel Buss. The polynomial hierarchy and intuitionistic bounded arithmetic. In Structure in Complexity, LNCS 233, pages 77–103, Berlin, 1986. Springer-Verlag.
3. [3] Peter Clote. A note on the relation between polynomial time functionals and constable’s class k. In Hans Kleine-B¨uning, editor, Computer Science Logic, LNCS 1092, pages 145–160, Berlin, 1996. Springer-Verlag.
4. [4] A. Cobham. The intrinsic computational difficulty of functions. In Y. Bar-Hillel, editor, Proceedings of the International Conference on Logic, Methodology, and Philosophy of Science, pages 24–30. North-Holland, Amsterdam, 1962.
5. Robert Constable. Type 2 computational complexity. In Fifth Annual ACM Symposium on Theory of Computing, pages 108–121, New York, 1973. ACM.
6. [6] Stephen Cook. Computability and complexity of higher type functions. In Y. Moschovakis, editor, Logic from Computer Science, pages 51–72. Springer- Verlag, New York, 1991.
7. [7] Stephen A. Cook and Alasdair Urquhart. Functional interpretations of feasible constructive arithemtic (extended abstract). In Proceedings of the 21st ACM Symposium on Theory of Computing, pages 107–112, 1989.
8. [8] Stephen A. Cook and Alasdair Urquhart. Functional interpretations of feasible constructive arithemtic. Annals of Pure and Applied Logic, 63:103–200, 1993.
9. [9] Steven Fortune. Topics in computational complexity. Phd dissertation, Cornell University, 1979.
10. [10] Steven Fortune, Daniel Leivant, and Michael O’Donnell. The expressiveness of simple and second-order type structures. Journal of the ACM, 30(1):151–185, January 1983.
11. [11] Jean-Yves Girard. Une extension de l’interprétation de Gödel à l’anal yse, et son application a l’élimination des coupures dans l’analyse et la théorie des types. In J.E. Fenstad, editor, Proceedings of the Second Scandinavian Logic Symposium, pages 63–92, Amsterdam, 1971. North-Holland.
12. [12] Kurt Gödel. Über eine bisher noch nicht benutzte erweiterung des finiten standpunktes. Dialectica, 12:280–287, 1958.
13. [13] A. Grzegorczyk. Some classes of recursive functions. In Rozprawy Mate. 4. Warsaw, 1953.
14. [14] R. Irwin, B. M. Kapron, and J. Royer. On characterizations of the basic feasible functionals part i. Journal of Functional Programming, 11:117–153, 2001.
15. [15] B. M. Kapron and S.A. Cook. A new characerization of type-2 feasibility. SIAM Journal of Computing, 25:117–132, 1996.
16. [16] Bruce Kapron and Stephen Cook. Characterizations of the basic feasible functionals of finite type. In S. Buss and P. Scott, editors, Feasible Mathematics, pages 71–95. Birkhauser-Boston, 1990.
17. [17] Daniel Leivant. Contracting proofs to programs. In P. Odifreddi, editor, Logic and Computer Science, pages 279–327. Academic Press, London, 1990.
18. [18] Daniel Leivant. A foundational delineation of poly-time. Information and Computation, 110:391–420, 1994. (Special issue of selected papers from LICS’91, edited by G. Kahn). Preminary report: A foundational delineation of computational feasibility, in Proceedings of the Sixth IEEE Conference on Logic in Computer Science, IEEE Computer Society Press, 1991.
19. [19] Daniel Leivant. Ramified recurrence and computational complexity I: Word recurrence and poly-time. In Peter Clote and Jeffrey Remmel, editors, Feasible Mathematics II, Perspectives in Computer Science, pages 320–343. Birkhauser- Boston, New York, 1994.
20. [20] Daniel Leivant. Termination proofs and complexity certification. In N. Kobayashi and B. Pierce, editors, Theoretical aspects of computer software, volume 2215 of LNCS, pages 183–200, Berlin, 2001. Springer-Verlag.
21. [21] Daniel Leivant. Calibrating computational feasibility by abstraction rank. In Gordon Plotkin, editor, Seventeenth IEEE Annual Symposium on Logic in Computer Science. IEEE Computer society Press, 2002.
22. [22] Daniel Leivant. Intrinsic reasoning about functional programs I: first order theories. Annals of Pure and Applied Logic, 114:117–153, 2002.
23. [23] Daniel Leivant and Jean-Yves Marion. Lambda calculus characterizations of poly-time. Fundamenta Informaticae, 19:167–184, 1993.
24. [24] Kurt Mehlhorn. Polynomial and abstract subrecursive classes. JCSS, 12:147–178, 1976.
25. [25] Michael O’Donnell. A programming language theorem which is independent of Peano Arithmetic. In Eleventh Annual ACM Symposium on Theory of Computing. ACM, 1979.
26. [26] John Reynolds. Towards a theory of type structures. In J. Loeckx, editor, Conference on Porgrammin, pages 408–425, Berlin, 1974.
27. Anil Seth. Some desirable conditions for feasible functionals of type 2. In Proceedings, Eighth Annual IEEE Symposium on Logic in Computer Science, pages 320–331, Washington, DC, 1993. IEEE Computer Society Press.