Author name cluster

Arend Rensink

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6 papers

2 author rows

I&C Journal 2007 Journal Article

Fair testing

Arend Rensink
Walter Vogler

In this paper we present a solution to the long-standing problem of characterising the coarsest liveness-preserving pre-congruence with respect to a full (TCSP-inspired) process algebra. In fact, we present two distinct characterisations, which give rise to the same relation: an operational one based on a De Nicola–Hennessy-like testing modality which we call should-testing, and a denotational one based on a refined notion of failures. One of the distinguishing characteristics of the should-testing pre-congruence is that it abstracts from divergences in the same way as Milner’s observation congruence, and as a consequence is strictly coarser than observation congruence. In other words, should-testing has a built-in fairness assumption. This is in itself a property long sought-after; it is in notable contrast to the well-known must-testing of De Nicola and Hennessy (denotationally characterised by a combination of failures and divergences), which treats divergence as catastrophic and hence is incompatible with observation congruence. Due to these characteristics, should-testing supports modular reasoning and allows to use the proof techniques of observation congruence, but also supports additional laws and techniques. Moreover, we show decidability of should-testing (on the basis of the denotational characterisation). Finally, we demonstrate its advantages by the application to a number of examples, including a scheduling problem, a version of the Alternating Bit-protocol, and fair lossy communication channels.

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I&C Journal 2001 Journal Article

Vertical Implementation

Arend Rensink
Roberto Gorrieri

We investigate criteria to relate specifications and implementations belonging to conceptually different levels of abstraction. For this purpose, we introduce the generic concept of a vertical implementation relation, which is a family of binary relations indexed by a refinement function that maps abstract actions onto concrete processes and thus determines the basic connection between the abstraction levels. If the refinement function is the identity, the vertical implementation relation collapses to a standard (horizontal) implementation relation. As desiderata for vertical implementation relations we formulate a number of congruence-like proof rules (notably a structural rule for recursion) that offer a powerful, compositional proof technique for vertical implementation. As a candidate vertical implementation relation we propose vertical bisimulation. Vertical bisimulation is compatible with the standard interleaving semantics of process algebra; in fact, the corresponding horizontal relation is rooted weak bisimulation. We prove that vertical bisimulation satisfies the proof rules for vertical implementation, thus establishing the consistency of the rules. Moreover, we define a corresponding notion of abstraction that strengthens the intuition behind vertical bisimulation and also provides a decision algorithm for finite-state systems. Finally, we give a number of small examples to demonstrate the advantages of vertical implementation in general and vertical bisimulation in particular.

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I&C Journal 2000 Journal Article

Bisimilarity of Open Terms

Arend Rensink

Traditionally, in process calculi, relations over open terms, i. e. , terms with free process variables, are defined as extensions of closed-term relations: two open terms are related if and only if all their closed instantiations are related. Working in the context of bisimulation, in this paper we study a different approach; we define semantic models for open terms, so-called conditional transition systems, and define bisimulation directly on those models. It turns out that this can be done in at least two different ways, one giving rise to De Simone's formal hypothesis bisimilarity and the other to a variation which we call hypothesis-preserving bisimilarity (denoted ∼fh and ∼hp, respectively). For open terms, we have (strict) inclusions ∼fh⊂∼hp⊂∼ci (the latter denoting the standard “closed instance” extension); for closed terms, the three coincide. Each of these relations is a congruence in the usual sense. We also give an alternative characterisation of ∼hp in terms of nonconditional transitions, as substitution-closed bisimilarity (denoted ∼sb). Finally, we study the issue of recursion congruence: we prove that each of the above relations is a congruence with respect to the recursion operator; however, for ∼ci this result holds under more restrictive conditions than for ∼fh and ∼hp.

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MFCS Conference 1997 Conference Paper

Dependency-Based Action Refinement

Arend Rensink
Heike Wehrheim

Abstract Action refinement in process algebras has been widely studied in the last few years as a means to support top-down design of systems. A specific notion of refinement arises when a dependency relation on the actions (in the Mazurkiewicz sense) is used to control the inheritance of orderings from the abstract level. In this paper we present a rather simple operational semantics for dependency-based 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.

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I&C Journal 1996 Journal Article

Comparing Syntactic and Semantic Action Refinement

Ursula Goltz
Roberto Gorrieri
Arend Rensink

The semantic definition of action refinement on labelled configuration structures is compared with the notion ofsyntactic substitution, which can be used as another notion of action refinement in a process algebraic setting. The comparison is done by studying a process algebra equipped with sequential composition, parallel composition with an explicit synchronisation set, and an operator for action refinement. On the one hand, the language (including the refinement operator) is given a configuration structure semantics. On the other hand, a reduction procedure transforms a process termPinto aflatterm (i. e. , with the refinement operator not occurring in it)red(P) by means of syntactic substitution, defined in a structural inductive way. The main aim of the paper is to investigate general conditions under which the termsPandred(P) have the same semantics. The results we present are essentially dependent on the question whether the refined action can be synchronised or not. In the latter case, Pandred(P) give rise to isomorphic configuration structures under mild assumptions. The former case is considerably more difficult, since then refinement cannot be expected to distribute over parallel composition. We give necessary and sufficientsemanticconditions under which distribution still holds up to semantic equivalence. Subsequently, we also give sufficient (but not necessary)syntacticconditions for reducible terms. Finally, we generalise these results to a language with recursion.

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TCS Journal 1994 Journal Article

Finite Petri nets as models for recursive causal behaviour

Ursula Goltz
Arend Rensink

Goltz (1988) discussed whether or not there exist finite Petri nets (with unbounded capacities) modelling the causal behaviour of certain recursive CCS terms. As a representative example, the following term is considered: B=(a. nil∣b. B)+c. nil. We will show that the answer depends on the chosen notion of behaviour. It was already known that the interleaving behaviour and the branching structure of terms as B can be modelled as long as causality is not taken into account. We now show that also the causal behaviour of B can be modelled as long as the branching structure is not taken into account. However, it is not possible to represent both causal dependencies and the behaviour with respect to choices between alternatives in a finite net. We prove that there exists no finite Petri net modelling B with respect to both pomset trace equivalence and failure equivalence.

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