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Constructing Exponentialsize Deterministic Zielonka Automata
 IN &QUOT;ICALP&QUOT;, VOL. LNCS 4052
, 2006
"... The wellknown algorithm of Zielonka describes how to transform automatically a sequential automaton into a deterministic asynchronous trace automaton. In this paper, we improve the construction of deterministic asynchronous automata from finite state automaton. Our construction improves the wellk ..."
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The wellknown algorithm of Zielonka describes how to transform automatically a sequential automaton into a deterministic asynchronous trace automaton. In this paper, we improve the construction of deterministic asynchronous automata from finite state automaton. Our construction improves the wellknown construction in that the size of the asynchronous automaton is simply exponential in both the size of the sequential automaton and the number of processes. In contrast, Zielonka’s algorithm gives an asynchronous automaton that is doubly exponential in the number of processes (and simply exponential in the size of the automaton).
Title: Studies in Comtrace Monoids
"... Mazurkiewicz traces were introduced by A. Mazurkiewicz in 1977 as a language representation of partial orders to model “true concurrency”. The theory of Mazurkiewicz traces has been utilised to tackle not only various aspects of concurrency theory but also problems from other areas, including combin ..."
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Mazurkiewicz traces were introduced by A. Mazurkiewicz in 1977 as a language representation of partial orders to model “true concurrency”. The theory of Mazurkiewicz traces has been utilised to tackle not only various aspects of concurrency theory but also problems from other areas, including combinatorics, graph theory, algebra, and logic. However, neither Mazurkiewicz traces nor partial orders can model the “not later than ” relationship. In 1995, comtraces (combined traces) were introduced by Janicki and Koutny as a formal language counterpart to finite stratified order structures. They show that each comtrace uniquely determines a finite stratified order structure, yet their work contains very little theory of comtraces. This thesis aims at enriching the tools and techniques for studying the theory of comtraces. Our first contribution is to introduce the notions of absorbing monoids, generalised comtrace monoids, partially commutative absorbing monoids, and absorbing monoids with compound generators, all of which are the generalisations of Mazurkiewicz trace
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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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.
Realizability of Concurrent Recursive Programs
, 2008
"... We define and study an automata model of concurrent recursive programs. An automaton consists of a finite number of pushdown systems running in parallel and communicating via shared actions. Actually, we combine multistack visibly pushdown automata and Zielonka’s asynchronous automata towards a mod ..."
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We define and study an automata model of concurrent recursive programs. An automaton consists of a finite number of pushdown systems running in parallel and communicating via shared actions. Actually, we combine multistack visibly pushdown automata and Zielonka’s asynchronous automata towards a model with an undecidable emptiness problem. However, a reasonable restriction allows us to lift Zielonka’s Theorem to this recursive setting and permits a logical characterization in terms of a suitable monadic secondorder logic. Building on results from Mazurkiewicz trace theory and recent work by La Torre, Madhusudan, and Parlato, we thus develop a framework for the specification, synthesis, and verification of concurrent recursive processes.
Weighted Distributed Systems and Their Logics
"... Abstract. We provide a model of weighted distributed systems and give a logical characterization thereof. Distributed systems are represented as weighted asynchronous cellular automata. Running over directed acyclic graphs, Mazurkiewicz traces, or (lossy) message sequence charts, they allow for mode ..."
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Abstract. We provide a model of weighted distributed systems and give a logical characterization thereof. Distributed systems are represented as weighted asynchronous cellular automata. Running over directed acyclic graphs, Mazurkiewicz traces, or (lossy) message sequence charts, they allow for modeling several communication paradigms in a unifying framework, among them probabilistic sharedvariable and probabilistic lossychannel systems. We show that any such system can be described by a weighted existential MSO formula and, vice versa, any formula gives rise to a weighted asynchronous cellular automaton. 1
Weighted asynchronous cellular automata
 In Proceedings of STACS 2006
, 2006
"... Abstract. We study weighted distributed systems whose behavior can be described as a formal power series over a free partially commutative or trace monoid. We characterize the behavior of such systems both, in the deterministic and in the nondeterministic case. As a consequence, we obtain a particu ..."
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Abstract. We study weighted distributed systems whose behavior can be described as a formal power series over a free partially commutative or trace monoid. We characterize the behavior of such systems both, in the deterministic and in the nondeterministic case. As a consequence, we obtain a particularly simple class of sequential weighted automata that have already the full expressive power. 1
Modular System Development With Pullbacks
, 2003
"... Two, seemingly different modular techniques for concurrent system development are investigated from a categorical perspective. A novel approach is presented in which they turn out to be merely special instances of pullback, a general categorical limit construction. Interestingly, the approach is ..."
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Two, seemingly different modular techniques for concurrent system development are investigated from a categorical perspective. A novel approach is presented in which they turn out to be merely special instances of pullback, a general categorical limit construction. Interestingly, the approach is based on truly concurrent semantics of systems.
Decidability Questions for Graph kCoverings
, 1997
"... . The notion of kcoverings of graphs, used previously in order to demonstrate some impossibility results for local graph computations, is investigated systematically. It turns out that, unlike the classical graph coverings where a simple method exists to construct them effectively for a given graph ..."
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. The notion of kcoverings of graphs, used previously in order to demonstrate some impossibility results for local graph computations, is investigated systematically. It turns out that, unlike the classical graph coverings where a simple method exists to construct them effectively for a given graph, kcoverings do not admit any such algorithm  the problem if a graph admits a nontrivial kcovering appears to be undecidable. 1 Introduction Our aim is to examine a special family of graph maps introduced in [12] and called kcoverings. By a graph we shall always mean an undirected simple graph G with a set V (G) of vertices and a set E(G) of edges, each edge e 2 E(G) being a pair e = fv; wg of two distinct vertices. Then a graph map f : H ! G from a graph H to a graph G is a mapping from V (H) [E(H) into V (G) [ E(G) such that  f maps vertices (edges) of H to vertices (respectively edges) of G and,  f preserves the adjacency between vertices and edges: if v 2 V (H) is adjacent...
On the confluence of trace rewriting systems
 PROCEEDINGS OF THE 18TH CONFERENCE ON FOUNDATIONS OF SOFTWARE TECHNOLOGY AND THEORETICAL COMPUTER SCIENCE, (FSTTCS'98), CHENNAI (INDIA), NUMBER 1530 IN LECTURE NOTES IN COMPUTER SCIENCE
, 1998
"... Trace rewriting systems, i.e., rewriting systems over trace monoids, generalize both semiThue systems and vector replacement systems. In [NO88], a particular trace monoid M is constructed such that confluence is undecidable for the class of lengthreducing trace rewriting systems over M. In this pa ..."
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Trace rewriting systems, i.e., rewriting systems over trace monoids, generalize both semiThue systems and vector replacement systems. In [NO88], a particular trace monoid M is constructed such that confluence is undecidable for the class of lengthreducing trace rewriting systems over M. In this paper, we show that this result holds for every trace monoid, which is neither free nor free commutative. Confluence for lengthreducing semiThue systems is shown to be Pcomplete. Furthermore we introduce a restricted notion of confluence, called (; )confluence, where ; 1. We prove that (; )confluence is decidable for trace rewriting sytems and use this result in order to obtain new classes of trace rewriting systems with a decidable confluence problem.
Asynchronous Games over Tree Architectures
, 2013
"... Abstract. We consider the distributed control problem in the setting of Zielonka asynchronous automata. Such automata are compositions of finite processes communicating via shared actions and evolving asynchronously. Most importantly, processes participating in a shared action can exchange complete ..."
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Abstract. We consider the distributed control problem in the setting of Zielonka asynchronous automata. Such automata are compositions of finite processes communicating via shared actions and evolving asynchronously. Most importantly, processes participating in a shared action can exchange complete information about their causal past. This gives more power to controllers, and avoids simple pathological undecidable cases as in the setting of Pnueli and Rosner. We show the decidability of the control problem for Zielonka automata over acyclic communication architectures. We provide also a matching lower bound, which is lfold exponential, l being the height of the architecture tree. 1