Las Vegas is better than determinism in VLSI and distributed computing

Abstract

In this paper we describe a new method for proving lower bounds on the complexity of VLSI - computations and more generally distributed computations. Lipton and Sedgewick observed that the crossing sequence arguments used to prove lower bounds in VLSI (or TM or distributed computing) apply to (accepting) nondeterministic computations as well as to deterministic computations. Hence whenever a boolean function f is such that f and f (the complement of f, f = 1 - f) have efficient nondeterministic chips then the known techniques are of no help for proving lower bounds on the complexity of deterministic chips. In this paper we describe a lower bound technique (Thm 1) which only applies to deterministic computations.