M. HENNESSY, Axiomatising finite concurrent processes, SIAM J. Comput., 17 (1988), pp. 997--1017.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....tress, called causal trees [DD89] See [BC87] for a good survey on the role of partial orders in semantics for concurrency. Apart from step semantics, di#erent proposals for generalizations of existing behavioural equivalences (for nondeterminism) have been made with time based equivalence [Hen88b] and distributed bisimulation [CH88, Kie89] among the most discriminating. See also the final remarks of these papers. Whereas the work on interleaving semantics has led to a number of e.g. axiomatisation and full abstractness results, such results are more unusual when it comes to ....

....bisimulation [CH88, Kie89] among the most discriminating. See also the final remarks of these papers. Whereas the work on interleaving semantics has led to a number of e.g. axiomatisation and full abstractness results, such results are more unusual when it comes to noninterleaving semantics, [Hen88b] and [CH88, Kie89] being among the few exceptions. Motivated by this we shall in this paper explore the possibility of defining natural operational semantics for a algebraic process language which at the same time open up opportunities for fully abstract denotational models with lpos as main ....

Matthew Hennessy. Axiomatising Finite Concurrent Processes. SIAM Journal on Computing, 17(5):997--1017, 1988.

....the characteristic contexts used to show full abstractness and expressive, we need to formalize the notion of fission refinement formulated in section 5 when finding the denotational models. Our notation for fission refinements, which splits an atomic action into two, is inspired by Hennessy [Hen87]. Now let a finite multiplicity function, m, be given and define n(m) max k k = 1 or #. m(a) k IN . Since # is infinite, but countable, there exists an injective function h : # S, F 1, n(m) #. For convenience we shall abbreviate h(#a, S, k#) by a S k and h(#a, F, ....

Matthew Hennessy. Axiomatising Finite Concurrent Processes. Technical Report 4/84, University of Sussex, 1987.

....scheme (3.8) to an axiom system makes the axiom system infinite; yet, it might make it complete too. Many researchers have attempted to replace (3. 8) by a finite collection of equational axioms, in the context of CCS [Moller 89] and other process algebras [Bergstra Klop 84, Bergstra Klop 85, Hennessy 87, Castellani Hennessy 89] For CCS, however, it is a result that any sound and complete axiomatisation for any process equivalence, which is at least as strong as , is of necessity infinite [Moller 89] This explains why the expansion law is taken apart from any system axiomatisation, and used ....

M. Hennessy. Axiomatising finite concurrent processes. Technical Report 4/87, University of Sussex, School of Computing Science, 1987.

....which has the poset derived from semantic normal forms as its representation of its compact elements. A similar approach occurs in Hennessy s model for testing equivalence based on finite acceptance 2 trees which basically is a syntax free representation of the syntactic normal forms he defines, [Hen85, Hen88b]. Yet another, and maybe the most mathematically elegant, way of defining a denotational model is to define it as the initial solution to a recursive domain equation. The normal forms may now occur in the description of the compact elements derived from this definition. In [Abr91] Abramsky ....

....a set of inference rules, Figure 3. We refer to the full proof system as E rec but the sub system where the rules ( and (rec) are omitted we call E. We write v Erec and v E for the induced preorders. The syntactic approximations p n , that occur in the rule ( are also standard (see e.g. [Hen88b]) and are defined inductively as follows: Definition 3.3 (Finite Syntactical Approximations) 1. u 0 = Omega for all u 2 TreeTerms. 2. a) nil n 1 = nil, Omega n 1 = Omega and x n 1 = x for x 2 Var, b) u 1 u 2 ) n 1 = u n 1 1 u n 1 2 , c) u) n 1 = u n 1 ) d) ....

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M. Hennessy. Axiomatising finite concurrent processes. SIAM Journal on Computing, 17(5):997--1017, 1988.

....as they occur in our theory, are not present in theories for action refinement. Aceto and Hennessy (1993) presented a complete axiomatisation for PA (including a special constant nil, being a hybrid of deadlock and empty process) with action refinement, modulo timed observational equivalence from Hennessy (1988). In this setting, laws such as a jj x a Delta x, which hold in standard PA, are no longer valid, as the atomic action a can be refined into any other process. This paper is set up as follows. In x2 we introduce the standard axioms of interleaving, and we prove that they do not form an ....

....prime generalised n term t such that (t z jj (u 00 ) oe m )v t jj ff k . Hence by Lemma 5.6 v ff l for some l 1. Consequently, v 00 ff l v 0 and by the induction hypothesis t 0 jj u 0 (t 00 jj u 00 )ff l ; hence, w 4 t. References Aceto, L. and Hennessy, M. 1993) Towards action refinement in process algebras. Information and Computation, 103(2) 204 269. Baeten, J. C. M. and Weijland, W. P. 1990) Process Algebra. Number 18 in Cambridge Tracts in Theoretical Computer Science. Cambridge University Press. Bergstra, J. A. and Klop, J. W. 1984) ....

Hennessy, M. (1988). Axiomatising finite concurrent processes. SIAM Journal of Computing , 17(5), 997--1017.

....the surprising result that performance equivalence can be reduced to a notion of equality of normal forms. For this, we use a decomposition approach along the lines that have been pioneered by [MM93] and which often work nicely in timed or normed settings (see Prop. 30 in [AM96] or Prop. 2.2. 8 in [Hen88]) The following lemma is the converse of Proposition 3.4. It emphasizes the link between the behaviours of the terms u and 1 . u. Lemma 5.1. 1 . u f 1 . v entails u f v. Proof. Standard: one checks that R def = f(u 1 ; u 2 ) j 1 . u 1 f 1 . u 2 g is an f performance equivalence. ut ....

M. Hennessy. Axiomatising finite concurrent processes. SIAM J. Comput., 17(5):997--1017, 1988.

....operator over the state construct : Notice that, while U and V are axiom schemata with an infinite number of possible instantiations, in every instantiation the summation Phi 0 is extended only to a finite number of summands. One comment relative to weak semantics is due. Referring to [Hen88], Luca Aceto discussed in [Ace94] the problems given raise by the interplay between the auxiliary constructs for expanding parallel compositions and the second Milner s law. Here the issue is completely avoided, as the ACP [BK84] merge operators are only used for the axiomatization A a of the ....

M. Hennessy. Axiomatising finite concurrent processes. SIAM Journal of Computing, 17(5):997--1017, 1988.

....of semantical equivalences, referred to as the linear time branching time spectrum is proposed by Van Glabbeek et al. cf. Gla90, Gla93, Gla96] In the context of the present paper the linear time notions of split n and ST bisimulation are relevant. Split semantics goes back at least to [Hen88]; two statements or structures are identified if they cannot be distinguished by splitting up their actions in sequences of actions up to length n. In ST bisimulation, as introduced in [GV87] the current state of a process distinguishes between the actions that have been completed and the ....

M. Hennessy. Axiomatising finite concurrent processes. SIAM Journal on Computing, 17:997--1017, 1988.

....and does not indicate formal relations between the equivalences in terms of implication. For example, it is not the case that pb is finer than STb ; in fact these notions are incomparable. Split bisimulation equivalence has been defined on a syntactical level on a subset of CCS in [Hennessy a]. In [AH b] it is established that it is preserved by action refinement on this subset. This does not contradict the negative result of [GV b] as in [vG a] it 7 [Vogler b] uses a restricted set of refinement functions, precluding the refinement by a parallel process that occurred in Example ....

M. Hennessy (1988): Axiomatising finite concurrent processes. SIAM Journal on Computing 17(5), pp. 997--1017.

.... Calcolo Parallelo e Informatica (obiettivo LAMBRUSCO) and Hewlett Packard Pisa Science Centre. y Dip. di Matematica Universit a di Bologna, P.zza di P. San Donato 5, I 40127 Bologna, Italy z Dip. di Informatica Universit a di Pisa, Corso Italia 40, I 56125, Pisa, Italy Hennessy [8] was probably the first who dropped the atomicity assumption from the standard bisimulation [12] by permitting actions to be observed in the middle of their evolution. In particular, he suggested atomic actions composed of two phases, their beginnings and their endings. This proposal can be ....

M. Hennessy. Axiomatising Finite Concurrent Processes. SIAM Journal on Computing, 17 (5), pages 997--1017, 1988.

.... testing bisimulation j j trace j 6 causality nondeterminism Figure 1: Traditional equivalences in tableau format. more and more prominence as possible candidates for congruences (thus permitting substitution of equals for equals ) w.r.t. suitable refinement operations. Hennessy [14] was probably the first who relaxed the atomicity assumption by permitting actions to be observed in the middle of their evolution. In particular, he suggested atomic actions composed of two phases, their beginnings and their endings. This proposal can be generalized to an arbitrary number of ....

M. Hennessy. Axiomatising finite concurrent processes. SIAM Journal on Computing, 17(5):997--1017, 1988.

....features of control flow in the setting of distributed systems. Some pointers to the literature in this area are [BGM91, Cho78, GG75, Gou83, How78, RW87] In the area of semantic models based on formalized notions of observation the first publications were by De Nicola and Hennessy [DNH84, DN87, Hen88] followed by work in a similar vein by Abramsky [Abr87] Many further publications can be found in this area, e.g. Phi87, Lan90b, LS88, Chr90] First publications dealing with the application of these semantic models to the problem of test derivation were given by Brinksma and Scollo [BSS87, ....

Matthew Hennessy. Axiomatising finite concurrent processes. SIAM Journal on Computing, 15(5):997--1017, October 1988.

....furthermore we have explicitly represented the possiblity that the two processes will be active at the same time. This matches our intuition about the behavior of independently executing computers. The idea of modelling durational events by pairs of instantaneous transitions is certainly not new [16, 17]. Technical difficulties arise when applying this approach to autoconcurrent Petri nets [25, 14] but because the process centered model of the next section by its very nature lacks autoconcurrency, we are able to use the split transition representation. 2.2 The Calculus Syntactic domains Term ....

M. Hennessy. Axiomatising finite concurrent processes. SIAM Journal of Computation, 15(5):997--1017, 1995.

....and still others on the assumption that actions have duration. In general, these three observational scenarios give rise to equivalences of incomparable discriminating power. In this paper, we show that three representative equivalences of the aforementioned classes, namely timed equivalence [Hen88], distributed bisimulation [CH89] and causal bisimulation [DD88] coincide over a language for finite parallel processes without communication and restriction. The proof of this result is algebraic in style and relies on a theorem giving a finite, complete axiomatization of causal bisimulation ....

.... and preserved by a very simple form of action refinement [AH89] 1 Introduction In recent years, many notions of equivalence for concurrent systems which distinguish concurrency from nondeterminism in the behaviour of processes have been proposed in the literature, e:g: timed bisimulation [Hen88], NMS bisimulation [DDNM87] distributed bisimulation [CH89] pomset bisimulation [BC88] ST bisimulation [GV87] history preserving bisimulation [RT88, GG89] and causal bisimulation [DD88] These proposals can be roughly divided into three main classes, depending on the kind of experiments which ....

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M. Hennessy. Axiomatising finite concurrent processes. SIAM Journal on Computing, 17(5):997--1017, 1988.

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M. HENNESSY, Axiomatising finite concurrent processes, SIAM J. Comput., 17 (1988), pp. 997--1017.

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M. Hennessy. Axiomatising finite concurrent processes. SIAM Journal on Computing, 17(5), 997--1017, October 1988. (pp 13, 33)

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M. Hennessy, Axiomatising finite concurrent processes, SIAM J. Comput. , 17 (1988), pp. 997--1017.

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