Article

Theory of Computing Systems

, Volume 48, Issue 1, pp 150-169

First online:

Parallelizing Time with Polynomial Circuits

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract

We study the problem of asymptotically reducing the runtime of serial computations with circuits of polynomial size. We give an algorithmic size-depth tradeoff for parallelizing time t random access Turing machines, a model at least as powerful as logarithmic cost RAMs. Our parallel simulation yields logspace-uniform t O(1) size, O(t/log t)-depth Boolean circuits having semi-unbounded fan-in gates. In fact, for appropriate d, uniform t O(1)2O(t/d) size circuits of depth O(d) can simulate time t. One corollary is that every log-cost time t RAM can be simulated by a log-cost CRCW PRAM using t O(1) processors and O(t/log t) time. This improves over previous parallel speedups, which only guaranteed an Ω(log t)-speedup with an exponential number of processors for weaker models of computation. These results are obtained by generalizing the well-known result that \(\textsf{DTIME}[t]\subseteq \textsf{ASPACE}[\log t]\).

Keywords

Circuit complexity Alternation Parallel speedup