Unique parallel decomposition in branching and weak bisimulation semantics

We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that totally normed behaviours always have parallel decompositions, but that these are not necessarily unique. Then, we establish that finite behaviours have unique parallel decompositions. We derive the latter result from a general theorem about unique decompositions in partial commutative monoids

Unique parallel decomposition in branching and weak bisimulation semantics

We consider the property of unique parallel decomposition modulo branching and weak bisimilarity. First, we show that normed behaviours always have parallel decompositions, but that these are not necessarily unique. Then, we establish that finite behaviours have unique parallel decompositions. We derive the latter result from a general theorem about unique decompositions in partial commutative monoids

Executable behaviour and the ππ-calculus

Reactive Turing machines extend Turing machines with a facility to model observable interactive behaviour. A behaviour is called executable if, and only if, it is behaviourally equivalent to the behaviour of a reactive Turing machine. In this paper, we study the relationship between executable behaviour and behaviour that can be defined in the $\pi$-calculus. We establish that executable behaviour is definable in the $\pi$-calculus up to a fine notion of behavioural equivalence that preserves all moments of choice and divergence. Moreover, we exhibit behaviour definable in the $\pi$-calculus that is not executable up to divergence-preserving behavioural equivalence. We do, however, obtain that every behaviour definable in the $\pi$-calculus is executable up to a divergence-insensitive notion of behavioural equivalence

On the executability of interactive computation

The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are reactively executable. In this article we provide a comparison of the two models. We show, on the one hand, that the behaviour exhibited by ITMs is reactively executable, and, on the other hand, that the stream translations naturally associated with RTMs are interactively computable. We conclude from these results that the theory of reactive executability subsumes the theory of interactive computability. Inspired by the existing model of ITMs with advice, which provides a model of evolving computation, we also consider RTMs with advice and we establish that a facility of advice considerably upgrades the behavioural expressiveness of RTMs: every countable transition system can be simulated by some RTM with advice up to a fine notion of behavioural equivalence

Up-to techniques for branching bisimilarity

\u3cp\u3eEver since the introduction of behavioral equivalences on processes one has been searching for efficient proof techniques that accompany those equivalences. Both strong bisimilarity and weak bisimilarity are accompanied by an arsenal of up-to techniques: enhancements of their proof methods. For branching bisimilarity, these results have not been established yet. We show that a powerful proof technique is sound for branching bisimilarity by combining the three techniques of up to union, up to expansion and up to context for Bloom’s BB cool format. We then make an initial proposal for casting the correctness proof of the up to context technique in an abstract coalgebraic setting, covering branching but also, delay and weak bisimilarity.\u3c/p\u3

Formal modelling and verification of an interlocking using mCRL2

\u3cp\u3eThis paper presents an application of the formal modelling and model checking toolkit mCRL2 and the model-based testing tool JTorX in the signalling domain. The mCRL2 toolkit is used to formally model the behaviour of a system at the core of signalling solutions: the interlocking. The model of the interlocking is validated through model-based testing. We use the mCRL2 toolkit to verify high-level safety properties of the interlocking software. The suitability of mCRL2, JTorX and our modelling approach is evaluated and suggestions are given for future research to improve the applicability of mCRL2 in the signalling domain.\u3c/p\u3

Sequential composition in the presence of intermediate termination:(Extended Abstract)

The standard operational semantics of the sequential composition operator gives rise to unbounded branching and forgetfulness when transparent process expressions are put in sequence. Due to transparency, the correspondence between context-free and pushdown processes fails modulo bisimilarity, and it is not clear how to specify an always terminating half counter. We propose a revised operational semantics for the sequential composition operator in the context of intermediate termination. With the revised operational semantics, we eliminate transparency, allowing us to establish a close correspondence between context-free processes and pushdown processes. Moreover, we prove the reactive Turing powerfulness of TCP with iteration and nesting with the revised operational semantics for sequential composition

Sequencing and intermediate acceptance:axiomatisation and decidability of bisimilarity

\u3cp\u3eThe Theory of Sequential Processes includes deadlock, successful termination, action prefixing, alternative and sequential composition. Intermediate acceptance, which is important for the integration of classical automata theory, can be expressed through a combination of alternative composition and successful termination. Recently, it was argued that complications arising from the interplay between intermediate acceptance and sequential composition can be eliminated by replacing sequential composition by sequencing. In this paper we study the equational theory of the recursion-free fragment of the resulting process theory modulo bisimilarity, proving that it is not finitely based, but does afford a ground-complete axiomatisation if a unary auxiliary operator is added. Furthermore, we prove that bisimilarity is decidable for processes definable by means of a finite guarded recursive specification over the process theory.\u3c/p\u3

Modelling and analysing ERTMS hybrid level 3 with the mCRL2 toolset

\u3cp\u3eERTMS Hybrid Level 3 is a recent proposal for a train control system specification that serves to increase the capacity of the railway network by allowing multiple trains with an integrity monitoring system and a GSM-R connection to the trackside on a single section. In this paper we model the principles of ERTMS Hybrid Level 3 in the mCRL2 process algebra and perform an analysis with its associated toolset. Our analysis has resulted in suggestions for improvement of the principles that will be taken into account in the next version of the specification.\u3c/p\u3