Abstract
A typed lambda calculus with recursion in all finite types is defined such that the first order terms exactlyc haracterize the parallel complexityclass NC. This is achieved byuse of the appropriate forms of recursion (concatenation recursion and logarithmic recursion), a ramified type structure and imposing of a linearity constraint.
Supported bythe DFG Graduiertenkolleg “Logik in der Informatik”
Supported bythe DFG Emmy Noether-Programme under grant No. Jo 291/2-1
The hospitalityof the Mittag-Leffler Institute in the spring of 2001 is gratefully acknowledged.
Supported bya Marie Curie fellowship of the European Union under grant no. ERBFMBI-CT98-3248
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References
B. Allen. Arithmetizing uniform NC. Annals of Pure and Applied Logic, 53(1):1–50, 1991.
S. Bellantoni. Predicative Recursion and Computational Complexity. PhD thesis, Universityof Toronto, 1992.
S. Bellantoni. Characterizing parallel time by type 2 recursions with polynomial output length. In D. Leivant, editor, Logic and Computational Complexity, pages 253–268. Springer LNCS 960, 1995.
S. Bellantoni and S. Cook. A new recursion-theoretic characterization of the polytime functions. Computational Complexity, 2:97–110, 1992.
S. Bellantoni, K.-H. Niggl, and H. Schwichtenberg. Higher type recursion, ramification and polynomial time. Annals of Pure and Applied Logic, 104:17–30, 2000.
S. Bellantoni and I. Oitavem. Separating NC along the δ axis. Submitted, 2001.
S. Bloch. Function-algebraic characterizations of log and polylog parallel time. Computational Complexity, 4:175–205, 1994.
P. Clote. Sequential, machine independent characterizations of the parallel complexity classes ALogTIME, AC k, NC k and NC. In S. Buss and P. Scott, editors, Feasible Mathematics, pages 49–69. Birkhäuser, 1990.
A. Cobham. The intrinsic computational difficultyof functions. In Proceedings of the second International Congress on Logic, Methodology and Philosophy of Science, pages 24–30, 1965.
K. Gödel. Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes. Dialectica, 12:280–287, 1958.
M. Hofmann. Programming languages capturing complexityclasses. ACM SIGACT News, 31(2), 2000. Logic Column 9.
M. Hofmann. Safe recursion with higher types and BCK-algebra. Annals of Pure and Applied Logic, 104:113–166, 2000.
D. E. Knuth. Sorting and Searching, volume 3 of The Art of Computer Programming. Addison-Wesley, 2nd edition, 1998.
D. Leivant. Stratified functional programs and computational complexity. In Proc. of the 20th Symposium on Principles of Programming Languages, pages 325–333, 1993.
D. Leivant. A characterization of NC bytree recurrence. In Proc. 39th Symposium on Foundations of Computer Science, pages 716–724, 1998.
D. Leivant and J.-Y. Marion. A characterization of alternating log time by ramified recurrence. Theoretical Computer Science, 236:193–208, 2000.
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Aehlig, K., Johannsen, J., Schwichtenberg, H., Terwijn, S.A. (2001). Linear Ramified Higher Type Recursion and Parallel Complexity. In: Kahle, R., Schroeder-Heister, P., Stärk, R. (eds) Proof Theory in Computer Science. PTCS 2001. Lecture Notes in Computer Science, vol 2183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45504-3_1
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