M. W. Shields. Concurrent machines. Computer Journal, 28:449-465, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....some conditions. Events with disjoint sets of related conditions are independent and may occur concurrently. Partially ordered structures which can be obtained by unfolding Petri nets, called processes (cf. Petri 77] represent runs of the modelled systems. Asynchronous transition systems (cf. Sh 85] and [Bedn 88] reflect the independence of events, but, similarly to usual transition systems, they abstract away from the internal structure of states and transitions. Equivalence classes of their paths that are obtained by reducing paths to the corresponding sequences of events and ignoring ....

Shields, E. W., Concurrent Machines, Computer Journal, vol. 28 (1985) 449-465

....pictured as follows: A 1 : A 2 : ffl ffl 10 repeating the same pattern infinitely to the left. Remarkably, the axioms of receptivity and monotonicity usually imposed on monotone port automata [30] and the usual commutativity axiom of asynchronous transition systems [4, 37] follow simply by functoriality for port automata of profunctors. B be a port profunctor. The following axioms hold for El (A;B) X) S; i; Gamma ; E) A1. Receptivity: 8e 2 IA ; s 2 S 9 s 2 S: s e Gamma s A2. Monotonicity: i a;v a;v A3. Commutativity: for e 1 ; ....

SHIELDS, M. W. Concurrent machines. Computer Journal 28 (1985), 449-- 465. 19

....the labelled nets of Fig. 1 [Old91] The leftmost net consists of two independent events labelled a and b, whereas the rightmost net is a purely (nondeterministic) sequential net. Many other closely related non interleaving models have been suggested, e.g. the asynchronous transition systems of [Bed88, Shi85] and the transitions systems with independence of [WN94] What is now the appropriate generalization of bisimulation to these INTRODUCTION 3 Figure 2: Labelled Petri nets representing a k b and a:b b:a. independence models Many attempts have been made to answer this question. Unfortunately, ....

M. W. Shields. Concurrent machines. Computer Journal, 88,

....Foundation. 1 t, then s t for some s 2 S. An asynchronous transition system is coherent if it satis es one further condition: t, and s t for some t 2 S. Asynchronous transition systems were introduced independently by Bednarczyk [Bed88] and Shields [Shi85]. Winskel and Nielsen [WN95, NW96] give a thorough survey and establish formal relationships between asynchronous transition systems and other models for concurrency, such as Petri nets, and event structures. The de nition of an asynchronous transition system may seem to be quite liberal, in the ....

M. W. Shields. Concurrent machines. Computer Journal, 28:449{ 465, 1985.

....if the paths are known to represent concurrency. The models of event structures, Petri nets and Mazurkiewicz trace languages mentioned above are all examples of independence models. So are the more direct extensions of transition systems as e.g. asynchronous transition systems ( 11] and [122]) and transition systems with independence ( 146] which are studied in Ch. 4 and Ch. 5. Finite versus infinite observations. In the majority of models for reactive systems, including all we have mentioned so far, infinite behaviours are completely determined by the finite behaviours. However in ....

....semantics to e.g. process calculi that takes independence information into account. The work in Ch. 4 and Ch. 5 investigate the formal relationship between two similar approaches, respectively the model of asynchronous transition systems, introduced independently by Bednarczyk [11] and Shields [122], and the model of transition systems with independence, proposed by Winskel and Nielsen [146] Both models have been applied to give SOS style independence semantics to CCS like calculi, respectively by Mukund and Nielsen in [93] using labelled asynchronous transition systems and Winskel and ....

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M. W. Shields. Concurrent machines. Computer Journal, 28:449--465, 1985.

....product and coproduct. The preservation properties of adjoints are helpful in showing, and explaining why, semantics is respected in moving from one model to another. A coreflection central to this paper is that embedding asynchronous transition systems, in the sense of Bednarczyk [1] and Shields [22], in Petri nets. The purpose of this paper is to illustrate the translation of concepts between models, focussing here on the transference of the concept of bisimulation to Petri nets from other models. The notion of bisimulation was defined categorically in [8] in a form directly applicable to a ....

....distinction between the pairs in terms of independence, we need to add some structure to the notion of case graph, here indicated by the I in the independent diamond. This is exactly the motivation behind asynchronous transition systems, as introduced independently by Bednarczyk [1] and Shields [22]. The idea on which they are based is simple enough: extend transition systems by, in addition, specifying which transitions are independent of each other. More accurately, transitions are to be thought of as occurrences of events which bear a relation of independence. Definition: An asynchronous ....

Shields, M.W., Concurrent machines. Computer Journal, vol. 28, pp. 449-- 465, 1985.

....(oe; x) if and only if (x) is undefined. 3 Asynchronous Automata Asynchronous Automata are a nice generalization of Mazurkiewicz traces, and have influenced a lot other models for concurrency (like transition systems with independence etc. They have been independently introduced in [27] and [2] The idea is to decorate transition systems with an independence relation (between actions) that will allow us to distinguish between true concurrency and mutual exclusion (or non determinism) of two actions. We actually use a slight modification for our purposes, due to [6] and called ....

M.W. Shields. Concurrent machines. Computer Journal, 28, 1985.

....that any precubical set can be seen as a (unlabelled) transition system, which is its 1 skeleton, on which we add independence relations. Filled in squares specify that two actions commute, i.e. that they can be run asynchronously. This is exactly the asynchronous automata sort of models [5] [54] and [41] Then in higher dimensions, we fill in cubes etc. meaning that we add some extra (n ary) independence relations. This is fully worked out in [28] in the form of adjunctions between suitable categories of transition systems and of asynchronous automata with (pre )cubical sets. In fact, to ....

Shields, M., Concurrent machines, Computer Journal 28 (1985).

.... o oo 0 M 0 in N 0 o oo 1 M . 1 (e) o oo 1 M 0 in N 1 ) Example: The productoftwo nets: 90 Chapter 10 Asynchronoustransition systems Asynchronoustransitionsystemsdeserve tobe betterknown asa modelof parallelcomputation.They wereintroducedindependentlyby Bednarczyk in[5]andShieldsin[84].The ideaonwhich theyarebasedissimpleenough: extendtransitionsystemsby,inaddition,specifyingwhich transitionsare independent ofwhich. More accurately, transitionsaretobe thought of asoccurrencesofeventswhich beara relationofindependence.Thisinterpretationissunnortedby axiomswhich ....

....ofconditionsand events) Morphismsareidentifledwith(partial)strategies.As wellasprovidinga reflnementofBerryandCurien ssequentialalgorithmsthenew categoriesaresuggestive ofnew paradigmsforcomputation. Asynchronoustr ansitionsystemsaredue toBednarczyk[5]and Shields[84] who discoveredthemindependently.Bednarczyk sthesis[5]containsthedeflnition ofthecategoryofasynchronoustransitionsystemsandthecoreectionswithevent structuresand Mazurkiewicztraces.Transitionsystemswithindependenceare relatedtotheconcurrenttransitionsystemsofStark[85] A related geometric approach ....

Shields,M.W., Concurrent machines,ComputerJournal,vol.28,pp. 449-465,1985.

....in the subject. Other potential applications of limits other than products are indicated in Section 7. In [3] the first two authors describe a method to synthesize a labelled 1 safe Petri net as an asynchronous realization of a concurrent behaviour described as an asynchronous system, cf. [1, 11]. In [8] Morin introduced a class of good asynchronous systems, which he calls concrete. Namely, an asynchronous system is concrete if it is isomorphic to a categorical product of sequential systems in the category of asynchronous systems with rigid morphisms. By definition, sequential systems ....

....of Winskel and flat meet preserving Petri net morphisms was used in [10] to establish an adjunction between elementary nets and elementary transition systems. In [15] flat meet preserving morphisms served the purpose to establish an adjunction between asynchronous transition systems, cf. [1, 11], and safe Petri nets. In this way we arrive at a small hierarchy of categories of Petri nets, cf. Figure 2. general multiplicative Winskel meet preserving flat meet preserving Winskel flat meet preserving Figure 2: A hierarchy of Petri net morphisms. The category of Petri nets with general ....

M. W. Shields. Concurrent machines. Computer Journal , vol. 28, pp. 449--465, 1985.

....from those in [Eb94] 1 . We note that in an automaton with global independence the concurrency of actions can be described by a single binary relation. These automata are only slight variants of the full trace automata and the asynchronous transition systems of Bednarczyk ( Be87] and Shields ([Sh85]) also, see e.g. St89b, St89c, WN94] for further results on this well studied class of automata. Even in this class, there are proper inclusions between the classes of first order definable and aperiodic, and between aperiodic and starfree languages. As shown in [Dr96] in an automaton without ....

M.W. Shields. Concurrent machines. Computer Journal, 28:449465, 1985.

....of trace based models like Mazurkiewitz traces [Maz88] synchronization trees [Mil80] Hoare languages [Hoa81] etc. Examples of the latter kind are Petri nets [BRG87] all kinds of transition systems like transition systems [Kel76] asynchronous transition systems [Bed88] concurrent machines [Shi85], trace automata [Shi85] transition systems with independence [SNW94] etc. We begin by looking at the most well known models (coming directly from the sequential world) i.e. the transition system based models. 1.1 A few transition systems 1.1.1 Ordinary transition systems Transition systems are ....

....like Mazurkiewitz traces [Maz88] synchronization trees [Mil80] Hoare languages [Hoa81] etc. Examples of the latter kind are Petri nets [BRG87] all kinds of transition systems like transition systems [Kel76] asynchronous transition systems [Bed88] concurrent machines [Shi85] trace automata [Shi85] transition systems with independence [SNW94] etc. We begin by looking at the most well known models (coming directly from the sequential world) i.e. the transition system based models. 1.1 A few transition systems 1.1.1 Ordinary transition systems Transition systems are one of the most famous ....

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M.W. Shields. Concurrent machines. Computer Journal, 28, 1985.

....look fora way ofequippingtransitionsystems witha notionof concurrency or independence ,inthesameway asLES may beseenasadding concurrency toST . Moreover,such enrichedtransitionsystemsshouldalsorepresent the systemmodel versionofevent 20 structures.Severalsuch modelshave appearedintheliterature[17,1,18]. Herewechooseavariationofthese,thetransitionsystemswithindependence. Transitionsystemswithindependencearetransitionsystemswithan independencerelationactuallycarriedby transitions.The novelty residesin thefactthatthenotionofeventbecomesnow a derived notion.However, ....

M.W. Shields.Concurrent Machines.ComputerJournal,n.28,pp. 449-465,1985.

....formulation of translation of properties is new. Also new is the formulation and use of the Reduction Lemmas. The notions of events and causality are not new [21, 30] Indeed, a variety of non interleaving models of concurrency have been proposed in the literature, such as partial orders of events [21, 34], event structures [30] Mazurkiewicz traces [26] and asynchronous transition systems [34] see [34] for a lucid exposition of the relationships between these models. While a great deal of theoretical investigation has been conducted, none of these works addresses the practical problem of how to ....

....Lemmas. The notions of events and causality are not new [21, 30] Indeed, a variety of non interleaving models of concurrency have been proposed in the literature, such as partial orders of events [21, 34] event structures [30] Mazurkiewicz traces [26] and asynchronous transition systems [34]; see [34] for a lucid exposition of the relationships between these models. While a great deal of theoretical investigation has been conducted, none of these works addresses the practical problem of how to verify realistic distributed algorithms using these models. We hope that this paper is a ....

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M.W. Shields, "Concurrent Machines", The Computer Journal , Vol. 28, No. 5, pp. 449--465, 1985.

....a b a a a b b c Fig. 1 Permutation and confluence properties given by independence of actions: from left to right, Comp1,Comp2,Comp3 axioms. In the deterministic case complete automata are also called asynchronous transition systems in (Winskel and Nielsen 1993) following [Bednarczyk, 1988] [Shields, 1985] and [Winskel and Nielsen, 1993] Comp1 et Comp2 impose the unicity condition for the states q et q 0 respectively, in the case we have two independent actions executable simultaneously. As recalled in the next lemma from Mazurkiewicz [Mazurkiewicz, 1986] only the first axiom and even ....

M.W. Shields. Concurrent machines. Computer Journal, 28, 1985.

.... models: Petri nets in many variations (cf. Reisig [16] various forms of event structures (cf. Nielsen et al. 15] Winskel [27] Boudol and Castellani [4] Langerak [11] Mazurkiewicz traces (cf. Mazurkiewicz [13] di erent forms of asynchronous transition systems (cf. Bednarczyk [1] Shields [18], Stark [19] Sassone et al. 17] causal trees (cf. Darondeau and Degano [5] As for equivalences, in addition to the natural isomorphisms over the above models, many of them are variations on i Initiated while the author was employed at the University of Twente; otherwise supported by the ....

M. W. Shields. Concurrent machines. The Computer Journal, 28(5):449-465, 1985.

....can also model phenomena like resolvable conflict that are not expressible by these event structures. Several brands of transition systems enriched with some auxiliary structure to capture causality have been proposed as models of concurrency, cf. the asynchronous transition systems of Shields [23] and Bednarczyk [2] the behaviour structures of Rabinovich Trakhtenbrot [21] the concurrent transition systems of Stark [24] and Droste, 5] and the transition systems with independence of Nielsen Winskel [26] In each of these cases the added structure does not fundamentally increase their ....

M.W. Shields (1985): Concurrent machines. The Computer Journal 28(5), pp. 449--465.

....are several candidates for the appropriate structures, and we turn now to consider one closely related to Petri nets. Models for Concurrency 39 9 Asynchronous transition systems Asynchronous transition systems 8 were introduced independently by Bednarczyk in (Bednarczyk 1988) and Shields in (Shields 1985). Their transitions are to be thought of as occurrences of events which bear a relation of independence. This interpretation is supported by axioms which essentially generalise those from Mazurkiewicz trace languages. Definition: An asynchronous transition system consists of (S, i, E, I, Tran) ....

Shields, M. W. (1985). Concurrent machines. Computer Journal, vol. 28.

.... independence of transitions in the marking graph of a safe net is then totally captured by a binary relation of independence on the set of actions (which are the labels of the transitions) Enriched with this relation, the marking graph becomes what is known as an Asynchronous Transition System [Bed88, Shi85]. For the converse direction, Nielsen and Winskel have defined a variant of region, called condition, in asynchronous transition systems (with the restriction that for every pair of independent actions there exists at least one state in which these actions are both enabled) Conditions of such an ....

Shields, M.W., Concurrent machines, Computer Journal, vol. 28 (1985) 449--465.

....associate each component with an automaton having vectors such as e as labels on transitions. This also paves the way for employing UML statecharts to describe the behaviour of software components. The automata we have in mind can be seen as elaborations of asynchronous transition systems [1, 23] and specialisations of hybrid transition systems [25] Further, it has been shown that every component generates such automata and every automaton generates a component. As a result, the component model may admit a complete au tomata theory. An automata theoretic view of composition is currently ....

M. W. Shields. Concurrent Machines. Computer Journal, 28:449--465, 1985.

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M. W. Shields. Concurrent machines. Computer Journal, 28:449-465, 1985.

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M. W. Shields. Concurrent machines. Computer Journal, 28:449-465, 1985.

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M. W. Shields. Concurrent machines. Computer Journal, 28:449--465, 1985.

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M. Shields. Concurrent machines. Computer Journal, 28:449--465, 1985.

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M. W. Shields. Concurrent machines. Computer Journal, 28:449--465, 1985.

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