Polynomial Synthesis of Asynchronous Automata

Zielonka's theorem shows that each regular set of Mazurkiewicz traces can be implemented as a system of synchronized processes with a distributed control structure called asynchronous automaton. This paper gives a polynomial algorithm for the synthesis of a non-deterministic asynchronous automaton from a regular Mazurkiewicz trace language. This new construction is based on an unfolding approach that improves the complexity of Zielonka's and Pighizzini's techniques in terms of the number of states.Comment: The MOdelling and VErification (MOVE) tea

A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications

Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modelling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behaviors of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin

Basic notions of universal algebra for language theory and graph grammars

AbstractThis paper reviews the basic properties of the equational and recognizable subsets of general algebras; these sets can be seen as generalizations of the context-free and regular languages, respectively. This approach, based on Universal Algebra, facilitates the development of the theory of formal languages so as to include the description of sets of finite trees, finite graphs, finite hypergraphs, tuples of words, partially commutative words (also called traces) and other similar finite objects

Asynchronous mappings and asynchronous cellular automata

International audienceThe aim of this paper is the study of asynchronous automata, a special kind of automata which encode the independency relation between actions and which enable their concurrent execution. These automata, introduced by Zielonka, constitute a natural extension of finite automata to the case of asynchronous parallelism. Their behaviour is described by trace languages, subsets of partially commutative monoids. The main result concerning this class of automata states that they accept exactly all recognizable trace languages. In this paper we give new improved constructions of asynchronous automata. In the final part of the paper we present a distributed system of messages with bounded time-stamps based on asynchronous automata