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Independence results in computer science

Authors:

J. Hartmanis,

J. E. HopcroftAuthors Info & Claims

ACM SIGACT News, Volume 8, Issue 4

Pages 13 - 24

https://doi.org/10.1145/1008335.1008336

Published: 01 October 1976 Publication History

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Abstract

In this note we show that instances of problems which appear naturally in computer science cannot be answered in formalized set theory. We show, for example, that some relativized versions of the famous P = NP problem cannot be answered in formalized set theory, that explicit algorithms can be given whose running time is independent of the axioms of set theory, and that one can exhibit a specific context-free grammar G for which it cannot be proven in set theory that L(G) = Σ* or L(G) ≠ Σ*.

References

[1]

Aho, A. V., J. E. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms," Addison-Wesley Publishing Co., Reading, Mass., 1974.

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[2]

Baker, T., J. Gill and R. Solovay, "Relativizations of the P = ?NP Question," SIAM J. on Comp. 4:4 (1975), pp. 431--442.

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[3]

Bernays, P., and A. A. Fraenkel, "Axiomatic Set Theory," North Holland Publ., Amsterdam, 1958.

Google Scholar

[4]

Blum, M., "A machine-independent theory of recursive functions," JACM 14:2 (1964), pp. 322--336.

Digital Library

Google Scholar

[5]

Hartmanis, J. and J. Simon, "On the structure of feasible computations" in Advances in Computers Vol. 14 (Edits. Morris Rubinoff and Marshall C. Yovits), Academic Press, New York, N.Y., 1976. pp. 1--43.

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[6]

Hopcroft, J. E. and J. D. Ullman, "Formal Languages and Their Relation to Automata," Addison-Wesley, Reading, Mass., 1969.

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Google Scholar

[7]

Matijasevic, Y. "Enumerable sets are Diophantine" (Russian), Dokl. Acad. Nauk. SSSR 191 (1970), pp. 279--282.

Google Scholar

[8]

Rogers, Hartly, Jr., "Theory of Recursive Functions and Effective Computability," McGraw-Hill, New York, N.Y., 1967.

Digital Library

Google Scholar

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Independence results in computer science
1. Theory of computation
  1. Models of computation
    1. Computability

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Published In

ACM SIGACT News Volume 8, Issue 4

October-December 1976

31 pages

ISSN:0163-5700

DOI:10.1145/1008335

Issue’s Table of Contents

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1976

Published in SIGACT Volume 8, Issue 4

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Liagkou VNastou PSpirakis PStamatiou Y(2022)How Hard Is It to Detect Surveillance? A Formal Study of Panopticons and Their Detectability ProblemCryptography10.3390/cryptography60300426:3(42)Online publication date: 20-Aug-2022
https://doi.org/10.3390/cryptography6030042
Yanofsky N(2022)Theoretical Computer Science for the Working Category Theorist10.1017/9781108872348Online publication date: 25-Jan-2022
https://doi.org/10.1017/9781108872348
Roush F(2022)An Algebraic Geometric Approach to NP ProblemsAdvances in Information and Communication10.1007/978-3-030-98012-2_29(387-398)Online publication date: 8-Mar-2022
https://doi.org/10.1007/978-3-030-98012-2_29
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Doria F(2018)El Aleph, Or a Monster Lurks in the Belly of Computer ScienceThe Map and the Territory10.1007/978-3-319-72478-2_22(403-417)Online publication date: 14-Feb-2018
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Kolokolova A(2017)Complexity Barriers as IndependenceThe Incomputable10.1007/978-3-319-43669-2_10(143-168)Online publication date: 6-May-2017
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Sigal R(2014)Undecidable complexity statements in -arithmeticThe Journal of Symbolic Logic10.2307/227485754:02(415-427)Online publication date: 12-Mar-2014
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Du DKo K(2014)ReferencesTheory of Computational Complexity10.1002/9781118595091.refs(458-479)Online publication date: 13-Jun-2014
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Calude CHromkovič J(2013)Complexity: A Language-Theoretic Point of ViewHandbook of Formal Languages10.1007/978-3-662-07675-0_1(1-60)Online publication date: 26-Mar-2013
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Du DKo K(2013)BibliographyTheory of Computational Complexity10.1002/9781118032916.biblio(453-473)Online publication date: 6-Dec-2013
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