Shields, M. Deterministic asynchronous automata. In E. J. Neuhold and G. Chroust (Eds.) Formal Methods in Programming, pp. 317--345, North-Holland, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the next Section. 4 Asynchronous systems with step semantics Let us formally introduce a more general model. We could continue with elementary transition systems, but there would be a price to pay. First, elementary transition systems are conceptually less suitable than asynchronous systems, see [12, 2], the model we are about to introduce. This is reflected not only in the number of axioms imposed in both cases. More importantly, the crucial notion of action independence is brought forward only in the definition of asynchronous systems, whereas it remains hidden in the structure of elementary ....

Shields, M. Deterministic asynchronous automata. In E. J. Neuhold and G. Chroust (Eds.) Formal Methods in Programming, pp. 317--345, North-Holland, 1985.

....decorated by concurrency, can be derived. In this paper, we bring together the works of [GV89] and [BD92] by defining truly concurrent behaviors. Namely, we describe truly concurrent models modulo a truly concurrent equivalence. The models we consider are Asynchronous Transition Systems (of [Shi85] and [Bed87] and the behavioral equivalence is ST bisimulation (of [GV87] Our appraoch has two main advantages : we deal with transition system like models, which is much more easy to understand than other approaches based on Petri nets or event structures, and we do not restrict to a ....

....specified Asynchronous Transition Systems (Lemma 3) which is used to prove the general congruence Theorem 1 for ST bisimulation of Section 4. We end by some concluding remarks. 1 Asynchronous Transition Systems We assume given a set of action names Act = fff; fi; fl : g [ fg. Definition 1. 1 ([Shi85], Bed87] A Labelled Asynchronous Transition System (ATS for short) over Act is a structure G = hS; E; I; li where ffl S = fs; u; s 1 ; s 2 : g is a set of states. ffl E = fa; b; e : g is a set of events. ffl I E Theta E is an irreflexive symmetric relation of independence between ....

M. W. Shields. Deterministic asynchronous automata. In Formal Methods in Programming. NorthHolland, 1985.

....in conflict: the occurrence of one of them forbids the occurrence of the other. From a causal point of view actions a and d must be sharing some locality. The approach we chose is to deduce the distribution of events from the semantics of a given process. We use asynchronous transition systems [14, 16] (ATS for short) to describe its behavior. Thus, in our case the architecture (i.e. the syntax) of the process is not known. Our contribution consists of the statement and exploration of this original semantic based approach. For each ATS we define an algebra of localities with a binary ....

....of ATS as well as some notions of graph theory. Section 3 introduces the algebra of localities. Six models for this algebra are presented in Section 4. Finally, conclusions and future works are given in Section 5. 2 Preliminaries Asynchronous Transitions Systems Asynchronous transition systems [14, 16] are a generalization of labeled transition systems. In ATSs, transitions are labeled with events, and each event represents a particular occurrence of an action. In addition, ATSs incorporate the idea of independent events. Two independent events can be executed in parallel, and so they cannot ....

M. Shields. Deterministic asynchronous automata. In Formal Methods in Programming. North-Holland, 1985.

....forget any information about any choices made in the past, even if some of this information is useless. We hope to overcome this problem by extending schedule automaton duality to structures in which conflict is not so permanent. One approach for doing this seems to be higher dimensional automata[Shi85, Pra91, GJ92], which distinguish a mutex b from ab ba by representing the former as a square with no interior, and the latter as in eks s with labelling. Eks s cannot make this distinction now, but higher dimensional automata do not yet have the schedule automata duality, and we hope to reconcile the two. We ....

M. Shields. Deterministic asynchronous automata. In E.J. Neuhold and G. Chroust, editors, Formal Models in Programming. Elsevier Science Publishers, B.V. (North Holland) , 1985.

....the rest at the initial state. 3 Geometric Automata 3. 1 Motivation The progenitor of the geometry of automata is the Poincare Liapounov Birkhoff geometry of dynamics [AS89, Bir27] More recent and relevant to computation is Papadimitriou s geometric model of concurrency control [Pap86] Shields [Shi85] refers briefly to geometrical automata, but the first detailed treatment of the notion is that of the present author [Pra91b] Consider the one event schedule a and its dual one transition automaton. Suppose that by looking more closely at a we find that it is really a sequence a 0 a 1 a 2 . The ....

M. Shields. Deterministic asynchronous automata. In E.J. Neuhold and G. Chroust, editors, Formal Models in Programming. Elsevier Science Publishers, B.V. (North Holland), 1985.

....of concurrent composition as interleaving may seem like a violation of true concurrency. The solution we have proposed elsewhere [Pra91b] to this apparent mismatch in the duality is to regard the product automaton as a 2D surface rather than a hollow square along the lines of [Pap86] and [Shi85]. We then derive dual (called perp in linear logic) as A = A Gammaffi 2. Next we obtain sum A B as the De Morgan dual of product, A B = A Theta B ) Sum and product are linear logic s additive connectives. We next define tensor product A Omega B via A Omega B = A ....

M. Shields. Deterministic asynchronous automata. In E.J. Neuhold and G. Chroust, editors, Formal Models in Programming. Elsevier Science Publishers, B.V. (North Holland) , 1985.

.... (Receptivity) For all states q and input actions e, there exists a state r such that r = T (q; e) These automata are closely related to the input output automata defined by Lynch and Tuttle [21] and also to the automata that have been studied by Bednarczyk [5] Kwiatkowska [20] and Shields [33]. A transition of A is a triple q e Gamma r, where r = T (q; e) We write t : q e Gamma r, or just q e Gamma r, to assert the existence of a transition t = q e Gamma r of A. Intuitively, a transition q e Gamma r represents a potential computation step of A in which action e occurs ....

M. W. Shields. Deterministic asynchronous automata. In E. J. Neuhold and G. Chroust, editors, Formal Methods in Programming, pages 317--345, North-Holland. 1985.

....of a monotone automaton requires that the concurrency information be reflected in the transition structure in a suitable sense. The particular automata used here have been studied previously by Stark [18, 17] Related automata have also been studied by Bednarczyk [2] Kwiatkowska [8] and Shields [14]. To define monotone automata, we first need the notion of a concurrent alphabet, which intuitively consists of a set of actions equipped with a description of which pairs of actions are concurrent or commuting. Formally, a concurrent alphabet is a set E, equipped with a symmetric, ....

M. W. Shields. Deterministic asynchronous automata. In Formal Methods in Programming, North-Holland. 1985.

.... to the input output automata defined by Lynch and Tuttle [10, 11] If we ignore the distinction between input and output actions, and we delete the monotonicity and receptivity conditions, we obtain automata similar to those that have been studied by Bednarczyk [2] Kwiatkowska [9] and Shields [19]. To further motivate the definitions, we describe how monotone input output automata can be used to model dataflow networks. For this, we use a restricted class of automata called monotone port automata, which are similar to the monotone port automata defined in [15] Formally, let us fix in ....

M. W. Shields. Deterministic asynchronous automata. In Formal Methods in Programming, North-Holland. 1985.

....distinctions can be made at the level of syntax, without resorting to reasoning about event occurrences. 1 Introduction This paper is part of an effort by many authors to give a truly concurrent semantics to process algebra. Many authors have previously contributed in this area, see e.g. [22, 19, 9, 20, 4, 11, 15, 1, 17, 2], and the methods have included translation into Petri nets, deriving an event structure, and enhancing the labels in labelled transition systems, often leading to descriptions of lowlevel character. We propose starting at the high level of abstraction usually associated with process algebras, and ....

M.W. Shields. Deterministic asynchronous automata. In Formal Methods in Programming. North Holland, 1985.

....of those processes. Our geometric view is closely related on the one hand to ST bisimulation [vGG89] and on the other to C. Papadimitriou s geometrical model for database concurrency control [Pap86, chap.6] Closer still is M. Shields proposal to add higher dimensional transitions to automata [Shi85], which D. Murphy brought to our attention too late for inclusion in the POPL 91 version of this paper. In the light of Shields work we see the chief contributions of the present paper as making a connection with homotopy and formally defining a suitable notion of higher dimensional automaton. To ....

M. Shields. Deterministic asynchronous automata. In E.J. Neuhold and G. Chroust, editors, Formal Models in Programming. Elsevier Science Publishers, B.V. (North Holland) , 1985.

....that most of the CSP laws are preserved, the exception being the expansion law and the idempotency of choice. 1 Introduction This paper is part of an effort by many authors to give a truly concurrent semantics to process algebra. Many authors have previously contributed in this area, see e.g. [16, 15, 9, 12, 4, 2, 14], and the methods have included translation into Petri nets, deriving an event structure, and enhancing the labels in labelled transition systems, often leading to descriptions of low level character. We propose starting at the high level of abstraction usually associated with process algebras, ....

....t 2 tr(P ) a = ld(s; t) s cf (P ) t; C7) s; X) 2 fail(P ) s; Y ) 2 fail(P ) s cf (P ) s ) s; X [ Y ) 2 fail(P ) If we observe sa and sb, and these do not conflict, then we expect also to observe sab and sba. This is the forward diamond property as seen in asynchronous transition systems [15] and elsewhere. This holds for CSP processes in our model. In fact, if P is constructed from 0, prefixing, k and n (so that P is conflict free) then we can also show sab co(P ) sba. However, as shown in Example 6.4, the stronger conclusion does not hold in general. Example 6.4 (Weak diamond ....

M.W. Shields. Deterministic asynchronous automata. In Formal Methods in Programming. North Holland, 1985.

....semantic model. As exhibited in some earlier papers of the author [12] non interleaving gives rise to the phenomenon of confusion, which is not present in standard interleaving descriptions of behaviour. We define a notion of a recursive (recursively enumerable) asynchronous transition system [25, 12] by enhancing it with concurrency information given in the form of a Mazurkiewicz independency relation [17] i.e. an irreflexive and symmetric relation on transitions) and show that our definition is indeed reasonable since such systems are determined by existing languages (e.g. Condition Event ....

....start and end states of consecutive transitions in a computation must agree, we cannot just permute two independent transitions because we would not necessarily obtain a valid computation. Instead, we require that a transition commutes with the residual of another transition. As introduced in [25, 12], we define an asynchronous transition system (abbrev. ATS) to be the structure S = Q; T; s; e; q 0 ) such that S = Q; T; s; e; q 0 ) is a rooted transition system, T Theta T is an independency relation, T Theta T Gamma T is an operation such that t 1 = t 2 is defined whenever ....

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M.W. Shields. Deterministic asynchronous automata. In Formal Methods in Programming. North Holland, 1985.

....distinctions can be made at the level of syntax, without resorting to reasoning about event occurrences. 1 Introduction This paper is part of an effort by many authors to give a truly concurrent semantics to process algebra. Many authors have previously contributed in this area, see e.g. [20, 17, 8, 18, 4, 9, 13, 1, 15, 2], and the methods have included translation into Petri nets, deriving an event structure, and enhancing the labels in labelled transition systems, often leading to descriptions of lowlevel character. We propose starting at the high level of abstraction usually associated with process algebras, and ....

M.W. Shields. Deterministic asynchronous automata. In Formal Methods in Programming. North Holland, 1985.

....problem of concurrency appears in its semantical dimension, disregarding complexities arisen from syntax and language definitions. Our contribution consists of stating and exploring this original semantic based approach. The behaviour of the process is described in asynchronous transition systems [2, 17] (ATS for short) For each ATS we define an axiomatisation that gives the minimal requirements to state whether two events must share some common place or not. The axiomatisation does not specify anything if such a statement cannot be deduced from the behaviour. The algebra has a binary ....

....relating the models and the usual operations for the ATS are introduced in Section 5. Finally, conclusions and future work are given in section 6. 2 Preliminaries a c b Fig. 1. The ATS for a:c:b:stop and a:c:stop jj c c:b:stop In this section we define the asynchronous transition systems [17, 2], the semantic model we are going to use. Then, we introduce graph theoretic notions and notations, based upon those of [8, 10] 2.1 Asynchronous Transitions Systems Asynchronous transition systems are a generalisation of labelled transition systems. In ATSs, transitions are labelled with events ....

M. Shields. Deterministic asynchronous automata. In Formal Methods in Programming. North-Holland, 1985.

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