Folk Theorems on the Correspondence between State-Based and Event-Based Systems

Kripke Structures and Labelled Transition Systems are the two most prominent semantic models used in concurrency theory. Both models are commonly believed to be equi-expressive. One can find many ad-hoc embeddings of one of these models into the other. We build upon the seminal work of De Nicola and Vaandrager that firmly established the correspondence between stuttering equivalence in Kripke Structures and divergence-sensitive branching bisimulation in Labelled Transition Systems. We show that their embeddings can also be used for a range of other equivalences of interest, such as strong bisimilarity, simulation equivalence, and trace equivalence. Furthermore, we extend the results by De Nicola and Vaandrager by showing that there are additional translations that allow one to use minimisation techniques in one semantic domain to obtain minimal representatives in the other semantic domain for these equivalences.Comment: Full version of SOFSEM 2011 pape

Reactive temporal logic

Whereas standard treatments of temporal logic are adequate for closed systems, having no run-time interactions with their environment, they fall short for reactive systems, interacting with their environments through synchronisation of actions. This paper introduces reactive temporal logic, a form of temporal logic adapted for the study of reactive systems. I illustrate its use by applying it to formulate definitions of a fair scheduler, and of a correct mutual exclusion protocol. Previous definitions of these concepts were conceptually much more involved or less precise, leading to debates on whether or not a given protocol satisfies the implicit requirements.Comment: In Proceedings EXPRESS/SOS 2020, arXiv:2008.1241

Bounded nondeterminism and the approximation induction principle in process algebra (extended abstract)

This paper presents a new semantics of ACPτ, the Algebra of Communicating Processes with abstraction. This leads to a term model of ACPτ which is isomorphic to the model of process graphs modulo rooted τδ-bisimulation of Baeten, Bergstra & Klop In this model, the Recursive Definition Principle (RDP), the Commutativity of Abstraction (CA) and Koomen's Fair Abstraction Rule (KFAR) are satisfied, but the Approximation Induction Principle (AIP) is not. The combination of these four principles is proven to be inconsistent, while any combination of three of them is not. In [2] a restricted version of AIP is proved valid in the graph model. This paper proposes a simpler and less restrictive version of AIP, not containing guarded recursive specifications as a parameter, which is still valid. This infinitary rule is formulated with the help of a family Bn of unary predicates, expressing bounded nondeterminism