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Asynchronous cellular automata for pomsets
 Theoretical Computer Science
, 1996
"... This paper extends to pomsets without autoconcurrency the fundamental notion of asynchronous cellular automata (ACA) which was originally introduced for traces by Zielonka. We generalize to pomsets the notion of asynchronous mapping introduced by Cori, Métivier and Zielonka and we show how to const ..."
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Cited by 19 (4 self)
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This paper extends to pomsets without autoconcurrency the fundamental notion of asynchronous cellular automata (ACA) which was originally introduced for traces by Zielonka. We generalize to pomsets the notion of asynchronous mapping introduced by Cori, Métivier and Zielonka and we show how to construct a deterministic ACA from an asynchronous mapping. Then we investigate the relation between the expressiveness of monadic second order logic, nondeterministic ACAs and deterministic ACAs. We can generalize Büchi’s theorem for finite words to a class of pomsets without autoconcurrency which satisfy a natural axiom. This axiom ensures that an asynchronous cellular automaton works on the pomset as a concurrent read and exclusive owner write machine. More precisely, in this class nondeterministic ACAs, deterministic ACAs and monadic second order logic have the same expressive power. Then we consider a class where deterministic ACAs are strictly weaker than nondeterministic ones. But in this class nondeterministic ACAs still capture monadic second order logic. Finally it is shown that even this equivalence does not hold in the class of all pomsets since there the class of recognizable pomset languages is not closed under complementation.
Deterministic Asynchronous Automata for Infinite Traces
 Acta Informatica
, 1993
"... 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 tra ..."
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Cited by 13 (3 self)
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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 Idiamond 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...
Some Combinatorial Aspects of TimeStamp Systems
 Europ. J. Combinatorics
, 1990
"... The aim of this paper is to outline a combinatorial structure appearing in distributed computing, namely a directed graph in which a certain family of subsets with k vertices have a successor. It has been proved that the number of vertices of such a graph is at least 2 k \Gamma 1 and an effective ..."
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Cited by 9 (4 self)
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The aim of this paper is to outline a combinatorial structure appearing in distributed computing, namely a directed graph in which a certain family of subsets with k vertices have a successor. It has been proved that the number of vertices of such a graph is at least 2 k \Gamma 1 and an effective construction has been given which needs k2 k\Gamma1 vertices. This problem is issued from some questions related to the labeling of processes in a system for determining the order in which they were created. By modifying some requirements on the distributed system, we show that there arise other combinatorial structures leading to the construction of solutions whose size becomes a linear function of the input. 0 Introduction Let us first describe in detail the problem of timestamping. In a system, we consider two kinds of events, namely the creation and the death of processes. We assume that two such events cannot occur simultaneously. A global "scheduler" assigns a timestamp to any proc...
Distributed games with causal memory are decidable for seriesparallel systems
 In FSTTCS ’04, LNCS 3328
, 2004
"... Abstract. This paper deals with distributed control problems by means of distributed games played on Mazurkiewicz traces. The main difference with other notions of distributed games recently introduced is that, instead of having a local view, strategies and controllers are able to use a more accurat ..."
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Cited by 7 (4 self)
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Abstract. This paper deals with distributed control problems by means of distributed games played on Mazurkiewicz traces. The main difference with other notions of distributed games recently introduced is that, instead of having a local view, strategies and controllers are able to use a more accurate memory, based on their causal view. Our main result states that using the causal view makes the control synthesis problem decidable for seriesparallel systems for all recognizable winning conditions on finite behaviors, while this problem with local view was proved undecidable even for reachability conditions. 1
Keeping Track of the Latest Gossip in a Distributed System
 DISTRIBUTED COMPUTING
, 1997
"... We tackle a natural problem from distributed computing, involving timestamps. 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: W ..."
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Cited by 6 (2 self)
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We tackle a natural problem from distributed computing, involving timestamps. 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 finitestate and local. Formally, this means that our algorithm can be implemented as an asynchronous automaton.
Distributed games and distributed control for asynchronous systems
 In LATIN04, volume 2976 of LNCS
, 2004
"... systems ..."
On Fireflies, Cellular Systems, and Evolware
"... Many observers have marveled at the beauty of the synchronous flashing of fireflies that has an almost hypnotic effect. In this paper we consider the issue of evolving twodimensional cellular automata as well as random boolean networks to solve the firefly synchronization task. The task was success ..."
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Cited by 4 (1 self)
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Many observers have marveled at the beauty of the synchronous flashing of fireflies that has an almost hypnotic effect. In this paper we consider the issue of evolving twodimensional cellular automata as well as random boolean networks to solve the firefly synchronization task. The task was successfully solved by means of cellular programming based coevolution performing computations in a completely local manner, each cell having access only to its immediate neighbor's states. An FPGAbased...
Unfolding Synthesis of Asynchronous Automata
 International Computer Science Symposium in Russia, CSR 2006. Available at http://www.cmi.univmrs.fr/˜morin/papers/CSR.pdf
"... Abstract. Zielonka’s theorem shows that each regular set of Mazurkiewicz traces can be implemented as a system of synchronized processes provided with some distributed control structure called an asynchronous automaton. This paper gives a new algorithm for the synthesis of a nondeterministic asynch ..."
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Cited by 3 (0 self)
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Abstract. Zielonka’s theorem shows that each regular set of Mazurkiewicz traces can be implemented as a system of synchronized processes provided with some distributed control structure called an asynchronous automaton. This paper gives a new algorithm for the synthesis of a nondeterministic asynchronous automaton from a regular Mazurkiewicz trace language. Our approach is based on an unfolding procedure that improves the complexity of Zielonka’s and Pighizzini’s techniques: Our construction is polynomial in terms of the number of states but still doubleexponential in the size of the alphabet. As opposed to Métivier’s work, our algorithm does not restrict to acyclic dependence alphabets.
Gossiping, Asynchronous Automata and Zielonka's Theorem
 SCHOOL OF MATHEMATICS, SPIC SCIENCE FOUNDATION
, 1994
"... In this paper, we first tackle a natural problem from distributed computing, involving timestamps. We then show that our solution to this problem can be applied to provide a simplified proof of Zielonka's theorema fundamental result in the theory of concurrent systems. Let P = fp 1 ; p 2 ; : ..."
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Cited by 3 (2 self)
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In this paper, we first tackle a natural problem from distributed computing, involving timestamps. We then show that our solution to this problem can be applied to provide a simplified proof of Zielonka's theorema 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 finitestate 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...