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Complexity classes of partial recursive functions (Preliminary Version)

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Edward L. RobertsonAuthors Info & Claims

STOC '71: Proceedings of the third annual ACM symposium on Theory of computing

Pages 258 - 266

https://doi.org/10.1145/800157.805055

Published: 03 May 1971 Publication History

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Abstract

This paper studies possible extensions of the concept of complexity class of recursive functions to partial recursive functions. Many of the well-known results for total complexity classes are shown to have corresponding, though not exactly identical, statements for partial classes. In particular, with two important exceptions, all results on the presentation and decision problems of membership for the two most reasonable definitions of partial classes are the same as for total classes. The exceptions concern presentations of the complements and maximum difficulty for decision problems of the more restricted form of partial classes.

The last section of this paper shows that it is not possible to have an “Intersection Theorem”, corresponding to the Union Theorem of McCreight and Meyer, either for complexity classes or complexity index sets.

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Cited By

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Tao R(1981)On the computational power of automata with time or space bounded by Ackermann's or superexponential functionsTheoretical Computer Science10.1016/0304-3975(81)90072-416:2(115-148)Online publication date: 1981
https://doi.org/10.1016/0304-3975(81)90072-4
Marchenkov SMatrosov V(1981)Complexity of algorithms and computationsJournal of Soviet Mathematics10.1007/BF0108428315:2(140-165)Online publication date: 1981
https://doi.org/10.1007/BF01084283
Meyer AMoll R(1972)Honest bounds for complexity classes of recursive functionsProceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)10.1109/SWAT.1972.8(61-66)Online publication date: 25-Oct-1972
https://dl.acm.org/doi/10.1109/SWAT.1972.8

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Classification of computable functions by primitive recursive classes
STOC '71: Proceedings of the third annual ACM symposium on Theory of computing

A classification of all the computable functions is given in terms of subrecursive programming languages. These classes are those which also arise from the relation “primitive recursive in.” By distinguishing between honest and dishonest classes the ...
Complexity classes of partial recursive functions

This paper studies possible extensions of the concept of complexity class of recursive functions to partial recursive functions. Many of the well-known results for total complexity classes are shown to have corresponding, though not exactly identical, ...
Recursive properties of abstract complexity classes (Preliminary Version)
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It is proven that complexity classes of abstract measures of complexity need not be recursively enumerable. However, the complement of each class is r.e.

Properties of effective enumerations of complexity classes are studied. For any measure there is ...

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STOC '71: Proceedings of the third annual ACM symposium on Theory of computing

May 1971

270 pages

ISBN:9781450374644

DOI:10.1145/800157

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

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Published: 03 May 1971

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STOC '71 Paper Acceptance Rate 23 of 50 submissions, 46%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

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Tao R(1981)On the computational power of automata with time or space bounded by Ackermann's or superexponential functionsTheoretical Computer Science10.1016/0304-3975(81)90072-416:2(115-148)Online publication date: 1981
https://doi.org/10.1016/0304-3975(81)90072-4
Marchenkov SMatrosov V(1981)Complexity of algorithms and computationsJournal of Soviet Mathematics10.1007/BF0108428315:2(140-165)Online publication date: 1981
https://doi.org/10.1007/BF01084283
Meyer AMoll R(1972)Honest bounds for complexity classes of recursive functionsProceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)10.1109/SWAT.1972.8(61-66)Online publication date: 25-Oct-1972
https://dl.acm.org/doi/10.1109/SWAT.1972.8

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Classification of computable functions by primitive recursive classes