The Power of the Queue

Queues, stacks, and tapes are basic concepts which have direct applications in compiler design and the general design of algorithms. Whereas stacks (pushdown store or last-in-rst-out storage) have been thoroughly investigated and are well understood, this is much less the case for queues ((rst-in-rst-out storage). In this paper we present a comprehensive study comparing queues to stacks and tapes (oo-line and with one-way input). The techniques we use rely on Kolmogorov complexity. In particular, 1 queue and 1 tape (or stack) are not comparable: (1) Simulating 1 stack (and hence 1 tape) by 1 queue requires (n 4=3 = log n) time in both the deterministic and the nondeterministic cases. (2) Simulating 1 queue by 1 tape requires (n 2) time in the deterministic case, and (n 4=3 =(log n) 2=3) in the nondeterministic case; We further compare the relative power between diierent numbers of queues: (3) Nondeterministically simulating 2 queues (or 2 tapes) by 1 queue requires (n 2 =(log 2 n log log n)) time and deterministically simulating 2 1 queues (or 2 tapes) by 1 queue requires (n 2) time. The second bound is tight. The rst is almost tight. We also obtain the upper bounds for queues. Below, we use \pushdown" and \stack" synonymously.