W. Zielonka, Notes on finite asynchronous automata, R.A.I.R.O.-Informatique Theorique et Applications, 21, 1987, 99-135.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....where each process i is capable of executing actions only among # i . These actions are used for communication among the processes or correspond to internal actions of a process (cf. Chapter 2) This leads us to the notion of a distributed alphabet, a notion due to Zielonka: Definition 3.1. 5 ( Zie87] A distributed alphabet # (over n processes) is an n tuple (# 1 , # n ) of (not necessarily disjoint) alphabets. For #, we let Proc( # ) denote the set . n . When the distributed alphabet is clear from the context, we simplify our notation and write Proc instead of Proc( # ....

....word. If Lw is trace consistent, it is clear that the set of linearizations of L t is identical to Lw . We conclude: Remark 3.5.3 Trace consistent regular languages can be identified with regular trace languages. A di#erent model characterizing regular trace languages was given by Zielonka [Zie87] It uses the notion of a distributed alphabet and of asynchronous automata. Its benefit is that the language accepted by an asynchronous automaton is a traceconsistent regular language and that for every trace consistent regular language, there is an asynchronous Buchi automaton accepting this ....

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W. Zielonka. Notes on finite asynchronous automata. R.A.I.R.O. --- Informatique Theorique et Applications, 21:99--135, 1987.

....MSC language is finitely generated. Following this, we establish that the class of finitely generated regular MSC languages coincides with the class of languages defined by locally synchronized MSGs. In one direction, this characterization hinges crucially on elements of Mazurkiewicz trace theory [8, 26]. In this paper we confine our attention to finite MSCs. We feel however that our results will serve as a good launching pad for a similar account concerning infinite MSCs. This should then lead to the design of appropriate temporal logics and automata theoretic solutions (based on ....

....by a B bounded message passing automaton. This is much harder to establish. # # be a regular MSC language. As observed at the end of Section 2, the minimum DFA for L yields a bound B such that L is B bounded. We first view L as a regular Mazurkiewicz trace language and apply Zielonka s theorem [26] to obtain a so called asynchronous automaton for L. We then convert into the desired B bounded message passing with the property L(A) L. 11 : Figure 3: The M i s accepted by the automaton in Figure 2. c#Ch be given by # c q p for c = p, q) We let X = P#Ch. ....

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Zielonka, W.: Notes on finite asynchronous automata. R.A.I.R.O. Informatique Theorique et Applications 21 (1987) 99--135

....one will have to use generalized versions of finite state automata. These process their inputs in a distributed fashion according to a distribution of actions, which we will introduce first. Following this, we introduce the class of automata called asynchronous automata as formulated by Zielonka [157] for recognizing regular languages of finite traces, and then subsequently define their generalization to infinite traces due to Gastin and Petit [43] We present a specific asynchronous automaton called the gossip automaton which plays an important role in some of the later developments. We then ....

....of finite traces accepted We will call the class of languages accepted by some asynchronous automaton the recognizable trace languages. Zielonka s fundamental result that asynchronous automata recognize exactly the regular trace languages can now be formulated Theorem 3.2. 2 (Zielonka [157]) Let TR # (#, I) Then is regular if and only if Tr (Z) for some asynchronous automaton Further, one may assume to be deterministic and one may assume # to be the distributed alphabet induced by the maximal D cliques of (#, I) 3.2.3 Asynchronous automata over infinite ....

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Zielonka, W.: Notes on finite asynchronous automata. R.A.I.R.O. Informatique Theorique et Applications 21 (

....L is recognizable if Gamma1 (L) Sigma 1 is recognizable in the usual sense for languages over Sigma 1 . The class of recognizable real trace languages is denoted by Rec(R( Sigma; D) A natural finite state device for trace languages is the asynchronous model introduced by Zielonka [21]. By asynchronous automata we mean two types of automata of equal expressive power, both of which have distributed control and memory. The difference consists mainly in the kind of restriction imposed on the concurrent access to common data. Asynchronous automata belong to the ....

....for any q; q 0 2 Q a2 Sigma Q a , u; v 2 Sigma with u j I v and q 0 2 ffi(q; u) also q 0 2 ffi(q; v) holds. Hence, we may define the trace language accepted by A by L(A) ft 2 M ( Sigma; D) j ffi(q 0 ; t) F 6= g. The asynchronous automaton model, as originally considered by Zielonka [21], associates to each letter a 2 Sigma a set dom(a) f1; mg of processors representing the read and write domain, such that (a; b) 2 I , dom(a) dom(b) An asynchronous automaton A is a tuple ( Q i ) m i=1 ; ffi a ) a2 Sigma ; q 0 ; F ) with a local transition relation ffi a ....

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W. Zielonka. Notes on finite asynchronous automata. R.A.I.R.O. --- Informatique Th'eorique et Applications, 21:99--135, 1987. 26

....systems which faithfully reflect the concurrency. For instance, Petri nets are a widely studied class of such transition systems. Asynchronous cellular automata (ACA) form another fundamental class of transition systems with built in concurrency. They were introduced for traces by Zielonka [Zie87, Zie89]. Mazurkiewicz introduced traces in order to describe the behaviors of one safe Petri nets [Maz77, Maz86] A trace is a pomset where the partial order is dictated by a static dependence relation over the actions of the system. The primary aim of this work is to generalize the notion of ACA so that ....

....definable pomset property that cannot be recognized by an ACA. Since the negation of this property is recognizable, we obtain that the class of recognizable pomset languages is not closed under complementation. The proofs of the positive results are based on the classical result by Zielonka [Zie87], on a close analysis of the pomsets and automata in consideration, and on a technique developed by Thomas [Tho90] for asynchronous automata for traces. The negative results are shown by separating examples. Preliminary versions of these results have appeared in the extended abstracts [DG96] and ....

W. Zielonka. Notes on finite asynchronous automata. R.A.I.R.O. - Informatique Th'eorique et Applications, 21:99--135, 1987.

....one will have to use generalized versions of finite state automata. These process their inputs in a distributed fashion according to a distribution of actions, which we will introduce first. Following this, we introduce the class of automata called asynchronous automata as formulated by Zielonka [157] for recognizing regular languages of finite traces, and then subsequently define their generalization to infinite traces due to Gastin and Petit [43] We present a specific asynchronous automaton called the gossip automaton which plays an important role in some of the later developments. We then ....

....accepting run of Z over T . We will call the class of languages accepted by some asynchronous automaton the recognizable trace languages. Zielonka s fundamental result that asynchronous automata recognize exactly the regular trace languages can now be formulated as Theorem 3.2. 2 (Zielonka [157]) Let L # TR # (#, I) Then L is regular if and only if L = L Tr (Z) for some asynchronous automaton Z over some e # where e # is a distributed alphabet whose induced trace alphabet is (#, I) Further, one may assume Z to be deterministic and one may assume e # to be the ....

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Zielonka, W.: Notes on finite asynchronous automata. R.A.I.R.O. Informatique Theorique et Applications 21 (1987) 99--135

....message that a creates during the third phase, u a = m; a; g) To show the correctness of fl it suffices to observe that if Condition ( Gamma ) holds for a history h then it holds for the history h(m; a) for every (m; a) 2 M Theta Sigma . 7. 7 Bibliographical Remarks Zielonka s Theorem is from [90]. Proofs based on the notion of asynchronous mappings can be found in [20, 24] and [34, Chapt.8] Asynchronous cellular automata have been introduced in [91] The transformations between different types of asynchronous automata have been studied in detail by Pighizzini [82] The construction for ....

Wies/law Zielonka. Notes on finite asynchronous automata. R.A.I.R.O. --- Informatique Th'eorique et Applications, 21:99--135, 1987.

....theory, see [AR88, Di90, DR94] for surveys. One of its foundational results ( Ma88] used in many difficult applications To appear in TCS96. An extended abstract of this work appeared in [BDK95] y Research supported by the German Research Foundation (DFG) 1 1: Introduction 2 (cf. [Oc85, Zi87, Di90, GRS91, Th90, EM95]) is that each element of the (algebraically defined) trace monoid has a graph theoretical representation. It is the aim of this paper to generalize this result and related versions of it to the context of automata with concurrency relations. Let us recall basic notions of trace theory and of ....

Zielonka, W.: Notes on finite asynchronous automata. R.A.I.R.O.-Informatique Th'eorique et Applications 21 (1987), 99-135.

....The decidability for Istl 3 can also be established by translating its formulas to a first order language of [3] that has variables ranging over local states, monadic predicates, and a binary partialorder relation. Alternatively, the 93 modality can be captured using asynchronous automata of [22], and complementation can be used to handle the dual. However, both these approaches lead to decision procedures of nonelementary complexity. Indeed, the translation from requirements on global cuts to linear sequences of local states is difficult due to various factors: a single local state can ....

W. Zielonka. Notes on finite asynchronous automata. R.A.I.R.O.-Informatique Th'eorique et Applications 21, 99--135, 1987.

.... trace languages to infinitary trace languages provided a characterization by concurrent rational expressions [14] Concerning recognition by means of finite state automata, a suitable model for trace languages is given by automata with distributed control, namely asynchronous (cellular) automata [26, 27]. With appropriate extensions of classical acceptance conditions (Buchi, Muller) it has been shown that the class of recognizable real trace languages corresponds to the family of languages accepted by non deterministic Buchi [13] respectively deterministic Muller asynchronous (cellular) ....

W. Zielonka. Notes on finite asynchronous automata. R.A.I.R.O. --- Informatique Th'eorique et Applications, 21:99--135, 1987.

....execution. Second, since finite acceptors of event structures are not known, no model checking method for event structure logics has been suggested. A first step towards connecting partial order executions with linearizations and automata was made in the definition of asynchronous Buchi automata [26]. These automata can be seen as recognizers of traces [9, 7] i.e. equivalence classes of linearizations of partial order executions) or alternatively directly recognizing the linearizations. A logic, called TrPtl, that is translatable to such automata was defined by Thiagarajan in [21] Our ....

....sequence in G such that g 0 2 G 0 , and g i g i 1 , for each i 0. Certain fairness restrictions can limit the set of program executions. One such fairness assumption that we will use in the sequel is the following: 1 A similar structure, called an asynchronousautomaton, was defined in [26] If some transition involving a process set X is continuously enabled from some state g i onwards, then some transition 0 involving at least one process from X is executed in some state g j with j i. This definition can be shown [7, 12] to be equivalent to requiring maximality of ....

W. Zielonka, Notes on finite asynchronous automata. R.A.I.R.O.-Informatique Th'eorique et Applications 21, 99--135, 1987.

....by means of recognizing morphisms [Gas91] and by c rational expressions [GPZ91] Concerning characterizations by finite automata, P. Gastin and A. Petit investigated asynchronous (cellular) automata for infinite traces [GP92] This type of automaton has been defined by W. Zielonka [Zie87, Zie89], who showed that for finite traces, the recognizable languages are exactly the languages recognized by deterministic asynchronous (cellular) automata. Asynchronous (cellular) automata have a decentralized control, which allows the parallel execution of independent actions. This concurrent ....

.... Gamma1 (s) j Gamma1 (e) L 6= j Gamma1 (s) j Gamma1 (e) L) Languages L IM of finite traces are called finitary in the following. For the family of finitary recognizable trace languages Rec(IM) W. Zielonka introduced the concept of asynchronous (cellular) automata ([Zie87], Zie89] and showed the deep result of the equivalence between Rec(IM) and the family of finitary trace languages accepted by deterministic asynchronous (cellular) automata. An asynchronous cellular automaton is a tuple A = Q a ) a2 Sigma ; ffi a ) a2 Sigma ; q 0 ; F ) where for each a 2 ....

W. Zielonka. Notes on finite asynchronous automata. R.A.I.R.O. --- Informatique Th'eorique et Applications, 21:99--135, 1987.

....of actions and parallelism of their execution [KMS91] In particular, even if our machines are deterministic, we can describe both synchronous and asynchronous devices by exploiting the rich structure of the alphabet. In fact, our machines generalize the asynchronous automata of Zielonka [Zie85]: the state space of this model of automata is given by a product and, in the description given by Zielonka, the alphabet is not structured. In our view, it is valuable to consider a more accurate description of the alphabet as a sum of products which allows us to express also the simultaneous ....

....to ensure that this semantic condition is satisfied. 3. Asynchrony In this section we show how two asynchronous devices can be described in our formalism. 3.1. Asynchronous automata One of the most widely studied automata theoretic models of concurrency are the asychronous automata of Zielonka [Zie85], which were introduced as recognizers of trace languages. Definition 3.1. An asynchronous automaton has a finite state space of the form X = X 1 Theta X 2 Theta Delta Delta Delta Theta Xn (i.e. n processors) Corresponding to each subset of the of the processors U f1; 2; ng ....

W. Zielonka. Notes on finite asynchronous automata. Informatique Th'eorique et Applications, 27:99--135, 1985.

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W. Zielonka, Notes on finite asynchronous automata, R.A.I.R.O.-Informatique Theorique et Applications, 21, 1987, 99-135.

....ABAA over e Sigma is the set of infinite sequences oe such that there exists an accepting execution ae over oe. Notice that because of non determinism there may be more than a single execution over a sequence oe. ABA are strongly related to similar models such as Buchi Asynchronous Automata [22] (which have more complicated acceptance conditions) and Asynchronous Buchi Cellular Automata [4] which have a local state space for each alphabet letter) The acceptance conditions of ABA are similar to those given in [13] for Asynchronous Buchi Cellular Automata, which simplify the ones ....

W. Zielonka, Notes on finite asynchronous automata, R.A.I.R.O.-Informatique Theorique et Applications, 21, 1987, 99-135.

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W. Zielonka. Notes on finite asynchronous automata. R.A.I.R.O.-Informatique Th eorique et Applications 21, 99--135, 1987.

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Zielonka, W.: Notes on finite asynchronous automata. R.A.I.R.O. Informatique Th'eorique et Applications 21 (1987) 99--135

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