P. Degano and R. Gorrieri. A causal operational semantics of action refinement.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....coupled similarity, does not abstract from keys. At least four techniques exist to enforce the necessary abstraction; they were developed over the past decade or so in di#erent specialisations, such as event based semantics (history preserving bisimilarity [22] and causal bisimilarity [16, 18, 12]) location based semantics (the so called static and dynamic approaches [1, 11, 14] and mobile calculi (the original semantics [48] and historydependent automata [50] Fresh keys are chosen canonically : for instance, one can assume a total ordering over Key and always use the smallest ....

P. Degano and R. Gorrieri. A causal operational semantics of action refinement. Information and Computation, 122:97--119, 1995.

....(maximally parallel) specification; he just has to fix the dependencies. In this setting, we also take another look at the concept of action refinement, in the shape of an operator that is not present in the standard algebras, but which has been the subject of extensive research: for instance, [3, 4, 26, 38, 39, 69, 76, 77]. The action refinement operator enables a designer to decompose abstract actions that are regarded as atomic, i.e. whose execution is modelled as an indivisible step, into more concrete behaviour that is no longer indivisible, but rather composed of many steps. This can be used as a tool in the ....

.... 4, we give a denotational counterpart, which is not based on an interleaving model but instead on an event based formalism developed in [66] We have chosen this type of model here because it allows us to use (variations on) standard constructions, especially for action refinement; see, e.g. [26, 38, 69]. In other words, our denotational model is certainly distinctive enough to capture all relevant behavioural effects of the operators of our algebra, including action refinement. We use a technique from metric semantics (see [23] for the denotation of recursive be haviour. We then show that the ....

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P. Degano and R. Gorrieri. A causal operational semantics of action refinement. Information and Computation, 122:97-119, 1995. 55

....equivalence, coupled similarity, does not abstract from keys. At least four techniques exist to enforce the necessary abstraction; they were developed over the past decade or so in di#erent specialisations, such as event based semantics (history preserving bisimilarity [22] and causal bisimilarity [16, 18, 12]) location based semantics (the so called static and dynamic approaches [1, 11, 14] and mobile calculi (the original semantics [48] and historydependent automata [50] Fresh keys are chosen canonically : for instance, one can assume a total ordering over Key and always use the smallest ....

P. Degano and R. Gorrieri. A causal operational semantics of action refinement. Information and Computation, 122:97--119, 1995.

....compact semantic models. Moreover we show that with this new pointer based technique it is possible to solve some problems that arise with the name technique when we extend our language with an action refinement operator P [a ; Q] which performs the semantic refinement of all a executed by P to Q [12,11,14]. In particular with the new technique we have that if both P and Q are finite state processes then P [a ; Q] is finite state. Through the new technique we define the ST semantics in SOS style for an extended language which includes the refinement operator and we produce a complete axiomatization ....

....association between actions a and processes Q is guaranteed by the fact that the events of starting and termination of each auto concurrent action e are uniquely related by the ST semantics. 9 9 This definition of semantic action refinement is slightly different from the usual definition [12,11,14] in that in P [a ; Q] each execution of Q is preceded and followed by the 13 Bravetti and Gorrieri ( P [a e] k feg; e ; Q; e Gamma 1 ) feg Gamma Gamma Gamma Gamma Gamma P 0 P [a ; Q] Gamma Gamma Gamma Gamma Gamma P 0 P ff Gamma Gamma Gamma Gamma Gamma P 0 P [ ....

P. Degano, R. Gorrieri, "A causal operational semantics of action refinement", in Information and Computation 122:97-119, 1995

....work in the setting of Petri nets is the full abstractness result of Jategaonkar and Meyer [JM92] with respect to testing equivalence. Other semantical investigations, driven by concrete process languages are, e.g. that of Aceto and Hennessy (cf. Ace90, AH93] and of Gorrieri [Gor91] see also [DG95]) The former is based on a syntactic interpretation of action refinement, a point of view not adopted here. For a discussion on the relationship between syntactic and semantic action refinement we refer to [GGR96] where also sufficient conditions are proposed for the coincidence of these ....

P. Degano and R. Gorrieri. A causal operational semantics of action refinement. Information and Computation, 122:97--119, 1995.

....that the definition of action refinement on causal trees is in agreement with the one on Delta free event structures, which is a special case of our operator on flow event structures. Operational definitions of action refinement are presented in [DG b, Rensink a c, BGG, CD a b] The treatment of [DG b] is shown to agree with the treatment of [DD c] in terms of causal trees. Likewise, Busi] shows that (a variant of) the treatment of [BGG] agrees with (a variant of) our treatments on flow and stable event structures. Action refinement has been defined on sets of pomsets a linear time variant ....

....and not in the associated interleaving model (which would be impossible according to Example 1.4) Forgetful refinement Because of the anomaly of Example 1.3, we have excluded refinement by the empty process. We know of three possibilities to deal with forgetful refinement nevertheless. In [DG b] refinement by an empty process is considered an erroneous step in the topdown development procedure, and is therefore identified with refinement by a deadlocked process. As we will allow refinement by deadlocked processes, our approach is equally general. In [BGG] a form of empty refinement on ....

P. Degano & R. Gorrieri (1995): A causal operational semantics of action refinement. Information and Computation 122(1), pp. 97--119.

....the technique compositionally. This allows us to define the ST semantics in SOS style for the basic process algebra and to produce a complete axiomatization for ST bisimulation over finite state processes. In the second part of the paper we extend our language with an action refinement operator [8, 6] P [a ; Q] which performs the semantic refinement of all a executed by P to Q, and we show that thanks to our technique it is possible to intuitively define such operator in term of the parallel operator and other basic operators. 2 The Basic Language Let A be a countable set of observable ....

P. Degano, R. Gorrieri, "A causal operational semantics of action refinement", in Information and Computation 122:97-119, 1995

....action refinement. We show the consistency of the operational with a (previously published) denotational semantics. We moreover show that bisimulation is a congruence for dependency based refinement. Finally, we give an illustrative example. 1 Introduction Action refinement in process algebras [1, 2, 18, 11, 8, 9] has been proposed to support hierarchical design of reactive systems. Starting with an abstract specification, step by step more concrete specifications are constructed by refining actions into concrete processes. Thus the complexity of the design process is reduced and furthermore verification ....

.... for Concurrency) For dependency based refinement, only the latter approach has been followed yet [14] In general, the two approaches do not coincide (for a comparison see [12] Operational semantics for action refinement, being consistent with a denotational model, have been defined in [6, 9, 22], however all of them generate transition systems with an enhanced labelling of transition (not just plain actions) adding e.g. causes or event names. The reason for this is essentially that plain transition systems can in general only be distinguished up to bisimulation and bisimulation is not ....

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P. Degano and R. Gorrieri. A causal operational semantics of action refinement. Information and Computation, 122(1):97--119, 1995.

....from features for encapsulating internal data structures and behaviour. In process algebraic frameworks, some structuring capabilities are provided by the term structure. Action refinement for the Pi calculus [Mil91] is presented in [AH93] General aspects of process refinement are dealt with in [DG91, DG95]. In [BK94] a concept for defining transactions as sequences of elementary actions in a logic programming style is defined, parallelism is modeled by interleaving. In [AH96] an abstract framework for reactive modules is presented which permits parallel composition and abstraction from the ....

P. Degano and R. Gorrieri. A Causal Operational Semantics of Action Refinement. Information and Computation, 122(1):97--119, 1995.

....we would like to develop vertical implementation relations that, given an abstract process S and a concrete process I , tell us if I is a possible implementation for the specification S. This problem is rather unexplored, with the exception of the work on action refinement in process algebra [1, 2, 12, 17, 35, 41, 42], which however is not satisfactory in some respects (to be discussed later) The main contribution of this paper is to single out some sensible criteria that any vertical implementation relation should satisfy. Furthermore, we introduce one specific instance of such a vertical relation, which we ....

.... theories say that the implementation of a specification S is given by r(S) the syntactic substitution of concrete processes r(a) for actions a in S) 1, 2, 21, 31] or by [ r] S] the semantic substitution of the semantics of concrete processes r(a) for actions a in the semantics of S) [12, 18, 22, 35]. Hence, the basic assumption of these theories is that there is only one possible implementation for a given specification; in other words, the action refinement function is used as a prescriptive tool to specify the only way abstract actions are to be implemented. Consequences of this are the ....

P. Degano and R. Gorrieri. A causal operational semantics of action refinement. Information and Computation, 122:97--119, 1995.

....that allows to obtain a simpler representation for states and more compact semantic models. Moreover we show that with this new pointer based technique it is possible to solve some problems that arise with the previous technique when we extend our language with an action refinement operator [7, 5] P [a ; Q] which performs the semantic refinement of all a executed by P to Q. In particular with the new technique we have that if P is a finite state process and Q is a finite state process then P [a ; Q] is finite state. Through the new technique we define the ST semantics in SOS style for an ....

P. Degano, R. Gorrieri, "A causal operational semantics of action refinement", in Information and Computation 122:97-119, 1995

....belong to the same alphabet. In the development of software components, however, it is quite often required to compare systems belonging to different abstraction levels. To the best of our knowledge, the only theory that has been developed to this aim is the work on action refinement (e.g. [2, 3, 7, 10, 18, 19, 20]) and interface refinement [4] Given a refinement function r mapping abstract actions to concrete processes, the developed theories say that the implementation of a specification S is given by the syntactic substitution of concrete processes r(a) for actions a in S [2, 3, 11, 16] or by the ....

.... processes, the developed theories say that the implementation of a specification S is given by the syntactic substitution of concrete processes r(a) for actions a in S [2, 3, 11, 16] or by the semantic substitution of the model of concrete processes r(a) for actions a in the semantics of S [7, 10, 12, 18]. The basic assumption of these theories is that there is only one possible implementation for a given specification; in other words, the action refinement function is used as a prescriptive tool to specify the only way abstract actions are to be implemented. Consequences of this are the ....

P. Degano and R. Gorrieri. A causal operational semantics of action refinement. I&C, 122:97--119, 1995.

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P. Degano and R. Gorrieri. A causal operational semantics of action refinement.

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