The Glory of the Past and Geometrical Concurrency

This paper contributes to the general understanding of the geometrical model of concurrency that was named higher dimensional automata (HDAs) by Pratt. In particular we investigate modal logics for such models and their expressive power in terms of the bisimulation that can be captured. The geometric model of concurrency is interesting from two main reasons: its generality and expressiveness, and the natural way in which autoconcurrency and action refinement are captured. Logics for this model, though, are not well investigated, where a simple, yet adequate, modal logic over HDAs was only recently introduced. As this modal logic, with two existential modalities, during and after, captures only split bisimulation, which is rather low in the spectrum of van Glabbeek and Vaandrager, the immediate question was what small extension of this logic could capture the more fine-grained hereditary history preserving bisimulation (hh)? In response, the work in this paper provides several insights. One is the fact that the geometrical aspect of HDAs makes it possible to use for capturing the hh-bisimulation, a standard modal logic that does not employ event variables, opposed to the two logics (over less expressive models) that we compare with. The logic that we investigate here uses standard past modalities and extends the previously introduced logic (called HDML) that had only forward, action-labelled, modalities. Besides, we try to understand better the above issues by introducing a related model that we call ST-configuration structures, which extend the configuration structures of van Glabbeek and Plotkin. We relate this model to HDAs, and redefine and prove the earlier results in the light of this new model. These offer a different view on why the past modalities and geometrical concurrency capture the hereditary history preserving bisimulation. Additional correlating insights are also gained.Comment: 17 pages, 7 figure

A Logical Verification Methodology for Service-Oriented Computing

We introduce a logical verification methodology for checking behavioural properties of service-oriented computing systems. Service properties are described by means of SocL, a branching-time temporal logic that we have specifically designed to express in an effective way distinctive aspects of services, such as, e.g., acceptance of a request, provision of a response, and correlation among service requests and responses. Our approach allows service properties to be expressed in such a way that they can be independent of service domains and specifications. We show an instantiation of our general methodology that uses the formal language COWS to conveniently specify services and the expressly developed software tool CMC to assist the user in the task of verifying SocL formulae over service specifications. We demonstrate feasibility and effectiveness of our methodology by means of the specification and the analysis of a case study in the automotive domain

On the Axiomatisation of Branching Bisimulation Congruence over CCS

In this paper we investigate the equational theory of (the restriction, relabelling, and recursion free fragment of) CCS modulo rooted branching bisimilarity, which is a classic, bisimulation-based notion of equivalence that abstracts from internal computational steps in process behaviour. Firstly, we show that CCS is not finitely based modulo the considered congruence. As a key step of independent interest in the proof of that negative result, we prove that each CCS process has a unique parallel decomposition into indecomposable processes modulo branching bisimilarity. As a second main contribution, we show that, when the set of actions is finite, rooted branching bisimilarity has a finite equational basis over CCS enriched with the left merge and communication merge operators from ACP

Analysis and Verification of Service Interaction Protocols - A Brief Survey

Modeling and analysis of interactions among services is a crucial issue in Service-Oriented Computing. Composing Web services is a complicated task which requires techniques and tools to verify that the new system will behave correctly. In this paper, we first overview some formal models proposed in the literature to describe services. Second, we give a brief survey of verification techniques that can be used to analyse services and their interaction. Last, we focus on the realizability and conformance of choreographies.Comment: In Proceedings TAV-WEB 2010, arXiv:1009.330

A Cancellation Law for Probabilistic Processes

We show a cancellation property for probabilistic choice. If distributions mu + rho and nu + rho are branching probabilistic bisimilar, then distributions mu and nu are also branching probabilistic bisimilar. We do this in the setting of a basic process language involving non-deterministic and probabilistic choice and define branching probabilistic bisimilarity on distributions. Despite the fact that the cancellation property is very elegant and concise, we failed to provide a short and natural combinatorial proof. Instead we provide a proof using metric topology. Our major lemma is that every distribution can be unfolded into an equivalent stable distribution, where the topological arguments are required to deal with uncountable branching.Comment: In Proceedings EXPRESS/SOS2023, arXiv:2309.0578

A Polynomial Time Algorithm for Deciding Branching Bisimilarity on Totally Normed BPA

Strong bisimilarity on normed BPA is polynomial-time decidable, while weak bisimilarity on totally normed BPA is NP-hard. It is natural to ask where the computational complexity of branching bisimilarity on totally normed BPA lies. This paper confirms that this problem is polynomial-time decidable. To our knowledge, in the presence of silent transitions, this is the first bisimilarity checking algorithm on infinite state systems which runs in polynomial time. This result spots an instance in which branching bisimilarity and weak bisimilarity are both decidable but lie in different complexity classes (unless NP=P), which is not known before. The algorithm takes the partition refinement approach and the final implementation can be thought of as a generalization of the previous algorithm of Czerwi\'{n}ski and Lasota. However, unexpectedly, the correctness of the algorithm cannot be directly generalized from previous works, and the correctness proof turns out to be subtle. The proof depends on the existence of a carefully defined refinement operation fitted for our algorithm and the proposal of elaborately developed techniques, which are quite different from previous works.Comment: 32 page