NDLI: The Power of the Queue

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The Power of the Queue

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Li, Ming Longpr, Luc Vitnyi, Paul
Copyright Year	1992
Abstract	Queues, stacks, and tapes are basic concepts that have direct applications in compiler design and the general design of algorithms. Whereas stacks (pushdown store or last-infirst-out storage) have been thoroughly investigated and are well understood, this is much less the case for queues (first-in-first-out storage). In this paper a comprehensive study comparing queues to stacks and tapes (off-line and with a one-way input tape) is presented. The techniques used rely on Kolmogorov complexity. In particular, one queue and one tape (or stack) are incomparable: (1) Simulating one stack (and hence one tape) by one queue requires $\Omega (n^{4/3} /\log n)$ time in both the deterministic and the nondeterministic cases. A corollary of this lower bound states that for this model of one-queue machines, nondeterministic linear time is not closed under complement. (2) Simulating one queue by one tape requires $\Omega (n^2 )$ time in the deterministic case and requires $\Omega (n^{4/3}/(\log n)^{2/3} )$ in the nondeterministic case.The paper further compares the relative power between different numbers of queues: (3) Simulating two queues (or two tapes) by one queue requires $\Omega (n^2 )$ time in the deterministic case, and $\Omega (n^2 /(\log ^2 n\log \log n))$ in the nondeterministic case. The deterministic bound is tight. The nondeterministic one is almost tight. The upper bounds for queues are also obtained.
Starting Page	697
Ending Page	712
Page Count	16
File Format	PDF
ISSN	00975397
DOI	10.1137/0221042
e-ISSN	10957111
Journal	SIAM Journal on Computing (SMJCAT)
Issue Number	4
Volume Number	21
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	on-line simulation Models of computation multi-tape machines Kolmogorov complexity upper bounds multi-queue machines lower bounds abstract storage unit Algorithmic information theory
Content Type	Text
Resource Type	Article
Subject	Mathematics Computer Science

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