Storage requirements for deterministic polynomialtime recognizable languages

Stephen Cook, Ravi Sethi

Research output: Contribution to journalArticle

56 Citations (Scopus)

Abstract

An intriguing question is whether (log n)2 space is enough to recognize the class {A figure is presented} of languages recognizable in deterministic polynomial time. This question has earlier been narrowed down to the storage required to recognize a particular language called SP. SP is clearly in {A figure is presented} and it has been shown that if SP has tape complexity (log n)k, then every member of {A figure is presented} has tape complexity (log n)k. This paper presents further evidence in support of the conjecture that SP cannot be recognized using storage (log n)k for any k. We have no techniques at present for proving such a statement for Turing machines in general; we prove the result for a suitably restricted device.

Original languageEnglish (US)
Pages (from-to)25-37
Number of pages13
JournalJournal of Computer and System Sciences
Volume13
Issue number1
DOIs
StatePublished - 1976
Externally publishedYes

Fingerprint

Tapes
Figure
Turing machines
Requirements
Turing Machine
Polynomials
Polynomial time
Language
Evidence
Class

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

Storage requirements for deterministic polynomialtime recognizable languages. / Cook, Stephen; Sethi, Ravi.

In: Journal of Computer and System Sciences, Vol. 13, No. 1, 1976, p. 25-37.

Research output: Contribution to journalArticle

@article{51c7ba46ac4544e0be16f449893994ad,
title = "Storage requirements for deterministic polynomialtime recognizable languages",
abstract = "An intriguing question is whether (log n)2 space is enough to recognize the class {A figure is presented} of languages recognizable in deterministic polynomial time. This question has earlier been narrowed down to the storage required to recognize a particular language called SP. SP is clearly in {A figure is presented} and it has been shown that if SP has tape complexity (log n)k, then every member of {A figure is presented} has tape complexity (log n)k. This paper presents further evidence in support of the conjecture that SP cannot be recognized using storage (log n)k for any k. We have no techniques at present for proving such a statement for Turing machines in general; we prove the result for a suitably restricted device.",
author = "Stephen Cook and Ravi Sethi",
year = "1976",
doi = "10.1016/S0022-0000(76)80048-7",
language = "English (US)",
volume = "13",
pages = "25--37",
journal = "Journal of Computer and System Sciences",
issn = "0022-0000",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Storage requirements for deterministic polynomialtime recognizable languages

AU - Cook, Stephen

AU - Sethi, Ravi

PY - 1976

Y1 - 1976

N2 - An intriguing question is whether (log n)2 space is enough to recognize the class {A figure is presented} of languages recognizable in deterministic polynomial time. This question has earlier been narrowed down to the storage required to recognize a particular language called SP. SP is clearly in {A figure is presented} and it has been shown that if SP has tape complexity (log n)k, then every member of {A figure is presented} has tape complexity (log n)k. This paper presents further evidence in support of the conjecture that SP cannot be recognized using storage (log n)k for any k. We have no techniques at present for proving such a statement for Turing machines in general; we prove the result for a suitably restricted device.

AB - An intriguing question is whether (log n)2 space is enough to recognize the class {A figure is presented} of languages recognizable in deterministic polynomial time. This question has earlier been narrowed down to the storage required to recognize a particular language called SP. SP is clearly in {A figure is presented} and it has been shown that if SP has tape complexity (log n)k, then every member of {A figure is presented} has tape complexity (log n)k. This paper presents further evidence in support of the conjecture that SP cannot be recognized using storage (log n)k for any k. We have no techniques at present for proving such a statement for Turing machines in general; we prove the result for a suitably restricted device.

UR - http://www.scopus.com/inward/record.url?scp=0016990118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016990118&partnerID=8YFLogxK

U2 - 10.1016/S0022-0000(76)80048-7

DO - 10.1016/S0022-0000(76)80048-7

M3 - Article

VL - 13

SP - 25

EP - 37

JO - Journal of Computer and System Sciences

JF - Journal of Computer and System Sciences

SN - 0022-0000

IS - 1

ER -