MOTIVATION Combinatorial effects, in which several variables jointly influence an output or response, play an important role in biological systems. In many settings, Boolean functions provide a natural way to describe such influences. However, biochemical data using which we may wish to characterize such influences are usually subject to much variability. Furthermore, in high-throughput biologi...

Boolean SAT problems are widespread in current demanding applications, most notably model checking for both hardware and software. It has long been known that the clause-to-variable ratio describes the likely behavior of randomly generated boolean formulae. This paper empirically investigates how the grouping of variables in these formulae further affects their satisfiability. keywords: normali...

It is well-known that all Boolean functions of n variables can be computed by a logic circuit with o(2n/n) gates (Lupanov's theorem) and that there exist Boolean functions of n variables which require logic circuits of this size (Shannon's theorem). We present corresponding results for Boolean functions computed by VLSI circuits, using Thompson's model of a VLSI chip. We prove that all Boolean ...

As they are conventionally formulated, Boolean games assume that players make their choices in ignorance of the choices being made by other players – they are games of simultaneous moves. For many settings, this is clearly unrealistic. In this paper, we show how Boolean games can be enriched by dependency graphs which explicitly represent the informational dependencies between variables in a ga...

The Boolean network can be used as a mathematical model for gene regulatory networks. An attractor, which is a state of a Boolean network repeating itself periodically, can represent a stable stage of a gene regulatory network. It is known that the problem of finding an attractor of the shortest period is NP-hard. In this article, we give a fixed-parameter algorithm for detecting a singleton at...