SPBC: a Markovian extension of finite Petri box calculus

Introducing the Iteration in sPBC

“…In this paper we have extended the operational and the denotational semantics that we presented in [14] for finite sPBC, by including the iteration operator, and considering the new version for the semantics of the synchronization operator, which is inspired in that one presented in [13].…”

“…Then, as we are using exponential distributions, the stochastic process associated with the evolution of every regular dynamic s-expression E is a Continuous Time Markov Chain (CTMC), which can be easily obtained from ts(E) in the same way as we showed in [14]: we modify the multigraph ts(E) by combining into a single edge all the edges connecting the same pair of nodes. These new edges will be labelled by the sum of the rates of the combined edges.…”

“…The description of a wider class of systems, such as real-time systems and fault-tolerance systems, is the goal of two timed extensions of PBC that we may find in the literature, namely tPBC [11] and TPBC [15], both of them considering a deterministic model of time. In the same line we presented sPBC in [14,13], which is a Markovian extension of PBC.…”

“…In our two previous works we only considered finite sPBC [14,13]. Then the aim of this paper is twofold: including in the syntax the iteration operator and proving that the operational and the denotational semantics (the latter based on a special kind of labelled SPNs, called s-boxes) are fully abstract.…”

“…For further details the reader is referred to the previous works of the authors [14,13]. The paper is structured as follows: in Section 2 we present an overview of the syntax.…”