An arithmetic for non-size-increasing polynomial-time computation

Theoretical Computer Science

Volumn 318, Issue 1-2, 2004, Pages 3-27

  Aehlig, Klaus ^a   Berger, Ulrich ^b   Hofmann, Martin ^a   Schwichtenberg, Helmut ^a  

^a UNIVERSITY OF MUNICH   (Germany)

^b SWANSEA UNIVERSITY   (United Kingdom)

Author keywords

Arithmetic; Higher types; Implicit computational complexity; Lambda calculus; Logic; Non size increasing polynomial time computation; Realizability

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; FORMAL LOGIC; THEOREM PROVING;

ARITHMETIC; HIGHER TYPES; IMPLICIT COMPUTATIONAL COMPLEXITY; LAMBDA CALCULUS; NON-INCREASING POLYNOMIAL TIME COMPUTATION; REALIZABILITY;

POLYNOMIALS;

EID: 2442444907     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2003.10.023     Document Type: Article

References (13)

1. K. Aehlig, H. Schwichtenberg, A syntactical analysis of non-size-increasing polynomial time computation, in: Proc. 15th IEEE Symp. on Logic in Computer Science (LICS '00), Santa Barbara, California, June 2000, pp. 84-91.
2. Bellantoni S., Niggl K.-H., Schwichtenberg H. Higher type recursion, ramification and polynomial time. Ann. Pure Appl. Logic. 104:2000;17-30.
3. Berger U. Program extraction from normalization proofs. Bezem M., Groote J.F. Typed Lambda Calculi and Applications. Lecture Notes in Computer Science. Vol. 664:1993;91-106 Springer, Berlin, Heidelberg, New York.
4. V.-H. Caseiro, Equations for defining poly-time functions, Ph.D. Thesis, University of Oslo, 1997. ftp.ifi.uio.no/pub/vuokko/ .
5. Gödel K. Über eine bisher noch nicht benützte Erweiterung des finiten Standpunkts. Dialectica. 12:1958;280-287.
6. M. Hofmann, Linear types and non-size-increasing polynomial time computation, in: Proc. 14th Symp. on Logic in Computer Science (LICS'99), Trento, Italy, 1999, pp. 464-473.
7. M. Hofmann, A type system for bounded space and functional in-place update. Nordic J. Programm., to appear, An extended abstract has appeared in: G. Smolka (Ed.), Programming Languages and Systems (Proc. ESOP 2000), Berlin, Lecture Notes in Computer Science, Springer, Berlin, 2000.
8. M. Hofmann, The strength of non-size-increasing computation, in: Proc. Principles of Programming Languages (POPL'02), Portland, Oregon, 2002.
9. Joachimski F., Matthes R. Short proofs of normalization for the simply-typed. λ -calculus, permutative conversions and Gödel's T Arch. Math. Logic. 42(1):2003;59-87.
10. Leivant D. Intrinsic reasoning about functional programs I. First order theories. Ann. Pure Appl. Logic. 114:2000;117-153.
11. J. van de Pol, Termination of higher-order rewrite systems, Ph.D. Thesis, Utrecht University, 1996.
12. Reddy U. Global state considered unnecessary. An introduction to object based semantics. J. Lisp Symbol. Comput. 9:1996;7-76.
13. J.C. Reynolds, Syntactic control of interference, in: ACM Symp. on Principles of Programming Languages, ACM, New York, 1978 pp. 39-46.