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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 infinit ..."
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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...
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 11 (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.
Muller MessagePassing Automata and Logics
, 2007
"... We study nonterminating messagepassing automata whose behavior is described by infinite message sequence charts. As a first result, we show that Muller, Büchi, and terminationdetecting Muller acceptance are equivalent for these devices. To describe the expressive power of these automata, we give ..."
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Cited by 4 (4 self)
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We study nonterminating messagepassing automata whose behavior is described by infinite message sequence charts. As a first result, we show that Muller, Büchi, and terminationdetecting 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 secondorder logic featuring a firstorder quantifier to express that there are infinitely many elements satisfying some property. Our result is based on a new extension of the classical EhrenfeuchtFraïssé game to cope with infinite structures and the new firstorder quantifier.
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 ..."
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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...
Finitestate Automata on Infinite Inputs
, 1996
"... This paper is a selfcontained introduction to the theory of finitestate automata on infinite words. The study of automata on infinite inputs was initiated by Büchi in order to settle certain decision problems arising in logic. Subsequently, there has been a lot of fundamental work in this area, re ..."
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This paper is a selfcontained introduction to the theory of finitestate automata on infinite words. The study of automata on infinite inputs was initiated by Büchi in order to settle certain decision problems arising in logic. Subsequently, there has been a lot of fundamental work in this area, resulting in a rich and elegant mathematical theory. In recent years, there has been renewed interest in these automata because of the fundamental role they play in the automatic verification Büchi initiated the study of finitestate automata working on infinite inputs in [Bü60]. He was interested in showing that the monadic second order logic of infinite sequences (S1S) was decidable. Büchi discovered a deep and elegant connection between sets of models of formulas in this logic and ωregular languages, the class of languages over infinite words
AssumptionCommitment in Automata
 Proc FST & TCS 17, LNCS 1346
, 1997
"... 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 certai ..."
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Cited by 2 (0 self)
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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 automatatheoretic 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 toplevel 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...
Distributed Muller Automata and Logics
, 2006
"... 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 firstorder quantifier to express that there are infinitely many elements s ..."
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Cited by 2 (2 self)
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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 firstorder quantifier to express that there are infinitely many elements satisfying some property. Our result is based on an extension of the classical EhrenfeuchtFraïssé game to cope with infinite structures and the new firstorder quantifier. As a byproduct, we obtain a logical characterization of unbounded Muller messagepassing automata running on infinite message sequence charts.
Determinizing Asynchronous Automata on Infinite Inputs
 APPEARS IN THIAGARAJAN, EDITOR, FOUNDATIONS OF SOFTWARE TECHNOLOGY AND THEORETICAL COMPUTER SCIENCE: 15TH CONFERENCE, FST&TCS '95 PROCEEDINGS, LNCS 1026
, 1995
"... Asynchronous automata are a natural distributed machine model for recognizing trace languageslanguages defined over an alphabet equipped with an independence relation. To handle ..."
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Asynchronous automata are a natural distributed machine model for recognizing trace languageslanguages defined over an alphabet equipped with an independence relation. To handle
Languages of infinite traces and deterministic asynchronous automata
, 2014
"... Abstract. In the theory of deterministic automata for languages of infinite words, a fundamental fact relates the family of infinitary limits of regular languages and the family of ωlanguages recognized by deterministic Büchi automata. With the known definitions of asynchronous automata, this obs ..."
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Abstract. In the theory of deterministic automata for languages of infinite words, a fundamental fact relates the family of infinitary limits of regular languages and the family of ωlanguages recognized by deterministic Büchi automata. With the known definitions of asynchronous automata, this observation does not extend to the context of traces. A major difficulty is posed by processes that stall after finitely many transitions. We introduce the family of deterministic, synchronizationaware asynchronous automata which – using as parameter the set of processes that stay live ad infinitum – allows us to settle an open question, namely, whether there exists a deterministic Büchi automaton recognizing precisely the infinitary limit of a regular trace language. Also, the corresponding class of unparameterized Muller automata captures all ωregular trace languages. 1