This paper shows the equivalence between the family of recognizable languages over infinite traces and the family of languages which are recognized by deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughton's Theorem from infinite words to infinite traces. Thereby we solve one of the main open problems in this field. As a special case we obtain that every closed (w.r.t. the independence relation) word language is accepted by some I-diamond deterministic Muller automaton. 1 Introduction A. Mazurkiewicz introduced the concept of traces as a suitable semantics for concurrent systems [Maz77]. A concurrent system is given by a set of atomic actions \Sigma = fa; b; c; : : :g together with an independence relation I ` \Sigma \Theta \Sigma, which specifies pairs of actions which can be performed concurrently. This leads to an equivalence relation on \Sigma generated by the independence relation I. More precisely, if a and b denote independent...

We tackle a natural problem from distributed computing, involving time-stamps. Let P = fp 1 ; p 2 ; : : : ; p N g be a set of computing agents or processes which synchronize with each other from time to time and exchange information about themselves and others. The gossip problem is the following: Whenever a set P ` P meets, the processes in P must decide amongst themselves which of them has the latest information, direct or indirect, about each agent p in the system. We propose an algorithm to solve this problem which is finite-state and local. Formally, this means that our algorithm can be implemented as an asynchronous automaton.

In this paper, we first tackle a natural problem from distributed computing, involving time-stamps. We then show that our solution to this problem can be applied to provide a simplified proof of Zielonka's theorem---a fundamental result in the theory of concurrent systems. Let P = fp 1 ; p 2 ; : : : ; p N g be a set of computing agents or processes which synchronize with each other from time to time and exchange information about themselves and others. The gossip problem is the following: Whenever a set P ` P meets, the processes in P must decide amongst themselves which of them has the latest information, direct or indirect, about each agent p in the system. We propose an algorithm to solve this problem which is finite-state and local. Formally, this means that our algorithm can be implemented as an asynchronous automaton. Solving the gossip problem appears to be a basic step in tackling other problems involving asynchronous automata. Here, we apply our solution to derive...

In the study of distributed systems, the assumption - commitment framework is crucial for compositional specification of processes. The idea is that we reason about each process separately, making suitable assumptions about other processes in the system. Symmetrically, each process commits to certain actions which the other processes can rely on. We study such a framework from an automata-theoretic viewpoint. We present systems of finite state automata which make assumptions about the behaviour of other automata and make commitments about their own behaviour. We characterize the languages accepted by these systems to be the regular trace languages (of Mazurkiewicz) over an associated independence alphabet, and present a syntactic characterization of these languages using top-level parallelism. The results smoothly generalize for automata over infinite words as well. 1 Introduction A distributed system usually consists of a finite number of processes, which proceed asynchronously and p...

Asynchronous automata are a natural distributed machine model for recognizing trace languages---languages defined over an alphabet equipped with an independence relation.

Abstract. We study nonterminating message-passing automata whose behavior is described by infinite message sequence charts. As a first result, we show that Muller, Büchi, and termination-detecting Muller acceptance are equivalent for these devices. To describe the expressive power of these automata, we give a logical characterization. More precisely, we show that they have the same expressive power as the existential fragment of a monadic second-order logic featuring a first-order quantifier to express that there are infinitely many elements satisfying some property. Our result is based on a new extension of the classical Ehrenfeucht-Fraïssé game to cope with infinite structures and the new first-order quantifier. 1

Abstract. We consider Muller asynchronous cellular automata running on infinite dags over distributed alphabets. We show that they have the same expressive power as the existential fragment of a monadic secondorder logic featuring a first-order quantifier to express that there are infinitely many elements satisfying some property. Our result is based on an extension of the classical Ehrenfeucht-Fraïssé game to cope with infinite structures and the new first-order quantifier. As a byproduct, we obtain a logical characterization of unbounded Muller message-passing automata running on infinite message sequence charts. 1