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Generalised Regular MSC Languages
 PROCEEDINGS OF THE 5TH INTERNATIONAL CONFERENCE ON FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES (FOSSACS’02), LECTURE NOTES IN COMPUTER SCIENCE 2303, SPRINGERVERLAG
, 2002
"... In this paper, we establish the concept of regularity for languages consisting of Message Sequence Charts (MSCs). To this aim, we formalise their behaviour by string languages and give a natural definition of regularity in terms of an appropriate Nerode right congruence. Moreover, we present a class ..."
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In this paper, we establish the concept of regularity for languages consisting of Message Sequence Charts (MSCs). To this aim, we formalise their behaviour by string languages and give a natural definition of regularity in terms of an appropriate Nerode right congruence. Moreover, we present a class of accepting automata and, using this characterisation, establish several decidability and closure properties of MSC languages. We also provide a logical characterisation by a monadic secondorder logic interpreted over MSCs. In contrast to existing work on regular MSC languages, our approach is neither restricted to a certain class of MSCs nor tailored to a fixed communication medium (such as a FIFO channel). It explicitly allows MSCs with message overtaking and is thus applicable to a broad range of channel types like mixtures of stacks and FIFOs.
Analysis of communicating automata
 In LATA 2010
, 2010
"... Abstract. This extended abstract is a survey of some of the recent developments in the area of automated verification dedicated to the analysis of communicating automata. Communicating automata are a fundamental computational model for concurrent systems, where processes cooperate via asynchronous ..."
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Abstract. This extended abstract is a survey of some of the recent developments in the area of automated verification dedicated to the analysis of communicating automata. Communicating automata are a fundamental computational model for concurrent systems, where processes cooperate via asynchronous message passing using unbounded channels. They are a popular model for representing and reasoning about communication protocols, and they have been used to define the semantics of standardized specification languages such as SDL. However, from the algorithmic point of view communicating automata are more challenging than other true concurrent models such as Petri nets: indeed, this model is Turing equivalent, in particular it subsumes Post tag systems [20]. Therefore, basic questions arising in formal verification, such as the reachability problem, are intractable. Solving the reachability problem is actually the first step in tackling the more general modelchecking problem, that consists in verifying that the model, i.e. the
General Morphisms of Petri Nets (Extended Abstract)
 Proc. Automata, Languages and Programming, 26th Intn'l Coll., Prague
, 1999
"... ) ? Marek A. Bednarczyk and Andrzej M. Borzyszkowski Institute of Computer Science, Gdansk Branch, Polish Acad. of Sc. Abrahama 18, 81825 Sopot, Poland, http://www.ipipan.gda.pl Abstract. A new notion of a general morphism of Petri nets is introduced. The new morphisms are shown to properly i ..."
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) ? Marek A. Bednarczyk and Andrzej M. Borzyszkowski Institute of Computer Science, Gdansk Branch, Polish Acad. of Sc. Abrahama 18, 81825 Sopot, Poland, http://www.ipipan.gda.pl Abstract. A new notion of a general morphism of Petri nets is introduced. The new morphisms are shown to properly include the morphisms considered so far. The resulting category of Petri nets is shown to admit products. Potential applications of general morphisms are indicated. 1 Introduction For mathematically oriented people Petri nets are quite complex objects. The following observation should put the above statement into a proper perspective: it took a quarter of a century from the inception of Petri nets, cf. [12], to the definition of their morphisms, cf. [14, 15]. Winskel's solution to the problem of defining a suitable notion of Petri net morphism was algebraic. He noticed that Petri nets can be viewed as certain 2sorted algebras. Consequently, Petri net morphisms defined in [14] are homomo...
Local LTL with past constants is expressively complete for Mazurkiewicz traces
 In Proc. of MFCS’03, number 2747 in LNCS
, 2003
"... Abstract. To obtain an expressively complete lineartime temporal logic (LTL) over Mazurkiewicz traces that is computationally tractable, we need to intepret formulas locally, at individual events in a trace, rather than globally, at configurations. Such local logics necessarily require past modalit ..."
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Abstract. To obtain an expressively complete lineartime temporal logic (LTL) over Mazurkiewicz traces that is computationally tractable, we need to intepret formulas locally, at individual events in a trace, rather than globally, at configurations. Such local logics necessarily require past modalities, in contrast to the classical setting of LTL over sequences. Earlier attempts at defining expressively complete local logics have used very general past modalities as well as filters (sideconditions) that “look sideways ” and talk of concurrent events. In this paper, we show that it is possible to use unfiltered future modalities in conjunction with past constants and still obtain a logic that is expressively complete over traces.
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
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
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.
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.