Abstract
Queues, stacks (pushdown stores), and tapes are storage models which have direct applications in compiler design and the general design of algorithms. Whereas stacks (pushdown store or last-in-first-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 we present a comprehensive study comparing queues to stacks and tapes. We address off-line machines with a one-way input. In particular, 1 queue and 1 tape (or stack) are not comparable:
(1) Simulating 1 stack (and hence 1 tape) by 1 queue requires Ω(n 4/3/logn) time in both the deterministic and the nondeterministic cases.
(2) Simulating 1 queue by 1 tape requires Ω(n 2) time in the deterministic case, and Ω(n 4/3/logn) in the nondeterministic case;
We further compare the relative power between different numbers of queues:
(3) Nondeterministically simulating 2 queues (or 2 tapes) by 1 queue requires Ω(n 2/(log2 n loglogn)) time and deterministically simulating 2 queues (or 2 tapes) by 1 queue requires Ω(n 2) time. The second bound is tight. The first is almost tight.
(4) We also obtain the simulation results for queues: 2 nondeterministic queues (or 3 pushdown stores) can simulate k queues in linear time. One queue can simulate k queues in quadratic time.
The work of the third author was supported in part by the Office of Naval Research under Contract N00014-82-K-0154, by the U.S. Army Research Office under Contracts DAAG29-79-C-0155 and DAAG29-84-K-0058, and by the National Science Foundation under Grant 832391-A01-DCR.
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Li, M., Longpré, L., Vitányi, P.M.B. (1986). The power of the queue. In: Selman, A.L. (eds) Structure in Complexity Theory. Lecture Notes in Computer Science, vol 223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16486-3_101
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DOI: https://doi.org/10.1007/3-540-16486-3_101
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