We prove lower bounds on the randomized two-party communication complexity of functions that arise from read-once boolean formulae. A read-once boolean formula is a formula in propositional logic with the property that every variable appears exactly once. Such a formula can be represented by a tree, where the leaves correspond ... more >>>

For circuit classes R, the fundamental computational problem, Min-R, asks for the minimum R-size of a boolean function presented as a truth table. Prominent examples of this problem include Min-DNF, and Min-Circuit (also called MCSP). We begin by presenting a new reduction proving that Min-DNF is NP-complete. It is significantly ... more >>>

We establish a lower bound of $\Omega{(\sqrt{n})}$ on the bounded-error quantum query complexity of read-once Boolean functions, providing evidence for the conjecture that $\Omega(\sqrt{D(f)})$ is a lower bound for all Boolean functions.Our technique extends a result of Ambainis, based on the idea that successful computation of a function requires ``decoherence'' ... more >>>

We prove the first time-space lower bound tradeoffs for randomized computation of decision problems. The bounds hold even in the case that the computation is allowed to have arbitrary probability of error on a small fraction of inputs. Our techniques are an extension of those used by Ajtai in his ... more >>>

Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the square-free numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing ... more >>>

We obtain the first non-trivial time-space tradeoff lower bound for functions f:{0,1}^n ->{0,1} on general branching programs by exhibiting a Boolean function f that requires exponential size to be computed by any branching program of length cn, for some constant c>1. We also give the first separation result between the ... more >>>