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The complexity of loop programs

Authors:

Albert R. Meyer and

Dennis M. RitchieAuthors Info & Claims

ACM '67: Proceedings of the 1967 22nd national conference

January 1967

Pages 465 - 469

https://doi.org/10.1145/800196.806014

Published: 01 January 1967 Publication History

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Abstract

Anyone familiar with the theory of computability will be aware that practical conclusions from the theory must be drawn with caution. If a problem can theoretically be solved by computation, this does not mean that it is practical to do so. Conversely, if a problem is formally undecidable, this does not mean that the subcases of primary interest are impervious to solution by algorithmic methods.

In the next section we describe such a class of programs, called “Loop programs.” Each Loop program consists only of assignment statements and iteration (loop) statements, the latter resembling the DO statement of FORTRAN, and special cases of the FOR and THROUGH statements of ALGOL and MAD. The bound on the running time of a Loop program is determined essentially by the length of the program and the depth of nesting of its loops.

References

[1]

M DAVIS Computability and unsolvability McGraw-Hill Book Company Inc New York 1958

Google Scholar

[2]

S C KLEENE Introduction to metamathematics Van Nostrand New York 1952

Google Scholar

[3]

P AXT Iteration of primitive recursion Abstract 597-182 Notices Amer Math Soc Jan. 1963

Google Scholar

[4]

A GRZEGORCZYK Some classes of recursive functions Rozprawy Matematyczne, Warsaw, 1953

Google Scholar

[5]

A R MEYER and D M RITCHIE Computational Complexity and Program Structure IBM Research Report, RC-1817.

Google Scholar

[6]

A R MEYER and D M RITCHIE Hierarchies of primitive recursive functions, in preparation

Google Scholar

[7]

A COBHAM The intrinsic computational difficulty of functions Proc of the 1964 Cong for Logic Meth and Phil of Science North-Holland, Amsterdam 1964

Google Scholar

[8]

R W RITCHIE Classes of predictably computable functions Trans Amer Math Soc Vol 106 Jan 1963 pp 139-173.

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Index Terms

The complexity of loop programs
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Logic programming and answer set programming
2. Theory of computation

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Published In

ACM '67: Proceedings of the 1967 22nd national conference

January 1967

607 pages

ISBN:9781450374941

DOI:10.1145/800196

Editor:
Solomon Rosenthal

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 January 1967

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https://doi.org/10.1080/17445760.2024.2347259
Palazzo MRoversi L(2024)Algorithmically Expressive, Always-Terminating Model for Reversible ComputationReversible Computation10.1007/978-3-031-62076-8_3(31-49)Online publication date: 29-May-2024
https://doi.org/10.1007/978-3-031-62076-8_3
Kulyukin V(2023)On the Computability of Primitive Recursive Functions by Feedforward Artificial Neural NetworksMathematics10.3390/math1120430911:20(4309)Online publication date: 16-Oct-2023
https://doi.org/10.3390/math11204309
Kulyukin V(2023)On Correspondences between Feedforward Artificial Neural Networks on Finite Memory Automata and Classes of Primitive Recursive FunctionsMathematics10.3390/math1112262011:12(2620)Online publication date: 8-Jun-2023
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Ernst HSchmidt JBeneken GErnst HSchmidt JBeneken G(2023)Algorithmen – Berechenbarkeit und KomplexitätGrundkurs Informatik10.1007/978-3-658-41779-6_12(521-575)Online publication date: 29-Nov-2023
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Kristiansen L(2022)Reversible computing and implicit computational complexityScience of Computer Programming10.1016/j.scico.2021.102723213:COnline publication date: 1-Jan-2022
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Leivant D(2021)Finitism, imperative programs and primitive recursionJournal of Logic and Computation10.1093/logcom/exaa076Online publication date: 28-Jan-2021
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Leivant D(2021)Algorithmically Broad Languages for Polynomial Time and SpaceLogic, Language, Information, and Computation10.1007/978-3-030-88853-4_23(372-387)Online publication date: 6-Oct-2021
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Ernst HSchmidt JBeneken GErnst HSchmidt JBeneken G(2020)Algorithmen – Berechenbarkeit und KomplexitätGrundkurs Informatik10.1007/978-3-658-30331-0_12(501-554)Online publication date: 10-Jul-2020
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Matos APaolini LRoversi L(2020)On the Expressivity of Total Reversible Programming LanguagesReversible Computation10.1007/978-3-030-52482-1_7(128-143)Online publication date: 9-Jul-2020
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