LIPIcs.FSCD.2019.29.pdf
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Pointers in Recursion: Exploring the Tropics
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4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Formal Structures for Computation and Deduction (FSCD) - License:
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- Publication Date: 2019-06-18
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I am grateful to the anonymous referees for their insightful and useful feedback.
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Paulin Jacobé de Naurois. Pointers in Recursion: Exploring the Tropics. In 4th International Conference on Formal Structures for Computation and Deduction (FSCD 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 131, pp. 29:1-29:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.FSCD.2019.29
https://doi.org/10.4230/LIPIcs.FSCD.2019.29
Abstract
We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent to the usual partial/primitive recursive functions. Complexity-wise, this framework captures in a streamlined way most of the relevant sub-polynomial classes. Pointer recursion with the safe/normal tiering discipline of Bellantoni and Cook corresponds to polylogtime computation. We introduce a new, non-size increasing tiering discipline, called tropical tiering. Tropical tiering and pointer recursion, used with some of the most common recursion schemes, capture the classes logspace, logspace/polylogtime, ptime, and NC. Finally, in a fashion reminiscent of the safe recursive functions, tropical tiering is expressed directly in the syntax of the function algebras, yielding the tropical recursive function algebras.
Subject Classification
ACM Subject Classification
- Software and its engineering → Recursion
- Theory of computation → Complexity theory and logic
- Theory of computation → Complexity classes
Keywords
- Implicit Complexity
- Recursion Theory
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References
- Bill Allen. Arithmetizing Uniform NC. Ann. Pure Appl. Logic, 53(1):1-50, 1991. URL: http://dx.doi.org/10.1016/0168-0072(91)90057-S.
-
S. Bellantoni. Predicative Recursion and Computational Complexity. PhD thesis, University of Toronto, 1992.
-
Stephen Bellantoni and Stephen A. Cook. A New Recursion-Theoretic Characterization of the Polytime Functions. Computational Complexity, 2:97-110, 1992.
- Stephen A. Bloch. Function-Algebraic Characterizations of Log and Polylog Parallel Time. Computational Complexity, 4:175-205, 1994. URL: http://dx.doi.org/10.1007/BF01202288.
- Guillaume Bonfante, Reinhard Kahle, Jean-Yves Marion, and Isabel Oitavem. Two function algebras defining functions in NC^k boolean circuits. Inf. Comput., 248:82-103, 2016. URL: http://dx.doi.org/10.1016/j.ic.2015.12.009.
- Ashok K. Chandra, Dexter Kozen, and Larry J. Stockmeyer. Alternation. J. ACM, 28(1):114-133, 1981. URL: http://dx.doi.org/10.1145/322234.322243.
-
P. Clote. Sequential, machine-independent characterizations of the parallel complexity classes ALOGTIME, AC^k, NC^k and NC. Feasible Mathematics, Birkhaüser, 49-69, 1989.
-
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.
- Martin Hofmann. Linear types and non-size-increasing polynomial time computation. Inf. Comput., 183(1):57-85, 2003. URL: http://dx.doi.org/10.1016/S0890-5401(03)00009-9.
- Martin Hofmann and Ulrich Schöpp. Pure pointer programs with iteration. ACM Trans. Comput. Log., 11(4):26:1-26:23, 2010. URL: http://dx.doi.org/10.1145/1805950.1805956.
- Satoru Kuroda. Recursion Schemata for Slowly Growing Depth Circuit Classes. Computational Complexity, 13(1-2):69-89, 2004. URL: http://dx.doi.org/10.1007/s00037-004-0184-4.
- Daniel Leivant. A Foundational Delineation of Computational Feasiblity. In Proceedings of the Sixth Annual Symposium on Logic in Computer Science (LICS '91), Amsterdam, The Netherlands, July 15-18, 1991, pages 2-11. IEEE Computer Society, 1991. URL: http://dx.doi.org/10.1109/LICS.1991.151625.
-
Daniel Leivant and Jean-Yves Marion. Ramified Recurrence and Computational Complexity II: Substitution and Poly-Space. In Leszek Pacholski and Jerzy Tiuryn, editors, CSL, volume 933 of Lecture Notes in Computer Science, pages 486-500. Springer, 1994.
- Daniel Leivant and Jean-Yves Marion. A characterization of alternating log time by ramified recurrence. Theor. Comput. Sci., 236(1-2):193-208, 2000. URL: http://dx.doi.org/10.1016/S0304-3975(99)00209-1.
- Daniel Leivant and Jean-Yves Marion. Ramified Recurrence and Computational Complexity IV : Predicative Functionals and Poly-Space. Information and Computation, page 12 p, 2000. to appear. Article dans revue scientifique avec comité de lecture. URL: https://hal.inria.fr/inria-00099077.
-
J. C. Lind. Computing in logarithmic space. Technical report, Massachusetts Institute of Technology, 1974.
- Peter Møller Neergaard. A Functional Language for Logarithmic Space. In Wei-Ngan Chin, editor, Programming Languages and Systems: Second Asian Symposium, APLAS 2004, Taipei, Taiwan, November 4-6, 2004. Proceedings, volume 3302 of Lecture Notes in Computer Science, pages 311-326. Springer, 2004. URL: http://dx.doi.org/10.1007/978-3-540-30477-7_21.
- Walter L. Ruzzo. On Uniform Circuit Complexity. J. Comput. Syst. Sci., 22(3):365-383, 1981. URL: http://dx.doi.org/10.1016/0022-0000(81)90038-6.