The model of bulk-synchronous parallel (BSP) computation is an emerging paradigm of general-purpose parallel computing. We study the BSP complexity of subcubic algorithms for Boolean matrix multiplication. The communication cost of a standard Strassen-type algorithm is known to be optimal

Boolean automata network. We show how these relate to some strong specific structural properties, thus supporting the idea that for most networks, synchronism only shortcuts asynchronous tra-jectories. We end with a discussion on the close relation that apparently exists between sensitivity to synchronism

Abstract. In this paper a spectral characterization of the synchroniza-tion property of Boolean dynamical systems is provided. Conditions on the spectrum of the next-state function are derived for two systems cou-pled in a unidirectional way- also called master-slave configuration-to guarantee self-synchronization

flow in synchronous languages. It is described here how to interpret Esterel programs as Boolean automata, and how these in turn yield Kripke structures. Model checking of CTL specifications is then a natural consequence of this interpretation. Keywords Synchronous languages, Esterel, Temporal logic

SynchronousBoolean relations can represent sequential don't care information in synchronous systems. These allow greater flexibility in expressing don't care information than ordinary Boolean relations. Synchronous relations can be used to specify sequential designs both at the finite

Flexibility in selecting the Boolean functions to implement a digital circuit has various forms which have been studied in the literature such as don't care conditions, Boolean relations, and synchronous recurrence equations. Each of these represents a particular degree of flexibility that may

Random Boolean networks (RBNs) are complex systems composed of many simple components which have been much analysed and shown to have many robust generic properties. Some synchronous versions have been influential as highly abstract models of specific biological systems, but for many biological

This paper characterizes the attractor structure of synchronous and asynchronous Boolean networks induced by bithreshold functions. Bi-threshold functions are generalizations of standard threshold functions and have separate threshold values for the transitions 0 → 1 (up-threshold) and 1 → 0 (down

In this paper are presented first results of a theoretical study on the role of non-monotone interac-tions in Boolean automata networks. We propose to analyse the contribution of non-monotony to the diversity and complexity in their dynamical behaviours according to two axes. The first one consists

makes this approach practically intractable for large programs. We introduce a strategy for dealing with this problem in the propositional case, corresponding e.g. to digital circuits and concurrent synchronization algorithms. Efficiently computable criteria are used to assess the mutual relevance