Nearly linear time

Yuri Gurevich; Saharon Shelah

doi:10.1007/3-540-51237-3_10

Nearly linear time

Yuri Gurevich, Saharon Shelah

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

66 Scopus citations

Abstract

The notion of linear-time computability is very sensitive to machine model. In this connection, we introduce a class NLT of functions computable in nearly linear time n(log n)^O(1) on random access computers. NLT is very robust and does not depend on the particular choice of random access computers. Kolmogorov machines, Schönhage machines, random access Turing machines, etc., also compute exactly NLT functions in nearly linear time. It is not known whether usual multitape Turing machines are able to compute all NLT functions in nearly linear time. We do not believe they are and do not consider them necessarily appropriate for this relatively low complexity level. It turns out, however, that nondeterministic Turing machines accept exactly the languages in the nondeterministic version of NLT. We give also a machine-independent definition of NLT and a natural problem complete for NLT.

Original language	English
Title of host publication	Logic at Botik 1989 - Symposium on Logical Foundations of Computer Science, Proceedings
Editors	Albert R. Meyer, Michael A. Taitslin
Publisher	Springer Verlag
Pages	108-118
Number of pages	11
ISBN (Print)	9783540512370
DOIs	https://doi.org/10.1007/3-540-51237-3_10
State	Published - 1989
Event	International Symposium on Logical Foundations of Computer Science, 1989 - PereslavI-Zalessky, Russian Federation Duration: 3 Jul 1989 → 8 Jul 1989

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	363 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Symposium on Logical Foundations of Computer Science, 1989
Country/Territory	Russian Federation
City	PereslavI-Zalessky
Period	3/07/89 → 8/07/89

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1989.

Access to Document

10.1007/3-540-51237-3_10

Cite this

Gurevich, Y., & Shelah, S. (1989). Nearly linear time. In A. R. Meyer, & M. A. Taitslin (Eds.), Logic at Botik 1989 - Symposium on Logical Foundations of Computer Science, Proceedings (pp. 108-118). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 363 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-51237-3_10

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Gurevich, Y & Shelah, S 1989, Nearly linear time. in AR Meyer & MA Taitslin (eds), Logic at Botik 1989 - Symposium on Logical Foundations of Computer Science, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 363 LNCS, Springer Verlag, pp. 108-118, International Symposium on Logical Foundations of Computer Science, 1989, PereslavI-Zalessky, Russian Federation, 3/07/89. https://doi.org/10.1007/3-540-51237-3_10

Nearly linear time. / Gurevich, Yuri; Shelah, Saharon.
Logic at Botik 1989 - Symposium on Logical Foundations of Computer Science, Proceedings. ed. / Albert R. Meyer; Michael A. Taitslin. Springer Verlag, 1989. p. 108-118 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 363 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Nearly linear time

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