Paweł Sobociński

Brendan Fong, Paolo Rapisarda, Paweł Sobociński

We develop a sound and complete graphical theory for discrete linear time-invariant dynamical systems. The graphical syntax, as in previous work, is closely related to the classical notion of signal flow diagrams, differently from previous work, these are understood as multi-input multi-output transducers that process streams with an \emph{infinite past} as well as an infinite future. This extended semantics features non-controllable systems, and we develop a novel, structural characterisation of controllability. Our approach is formalised through the theory of props, extending the work of Bonchi, Zanasi and the third author.

Paweł Sobociński

Compositionality and process equivalence are both standard concepts of process algebra. Compositionality means that the behaviour of a compound system relies only on the behaviour of its components, i.e. there is no emergent behaviour. Process equivalence means that the explicit statespace of a system takes a back seat to its interaction patterns: the information that an environment can obtain though interaction. Petri nets are a classical, yet widely used and understood, model of concurrency. Nevertheless, they have often been described as a non-compositional model, and tools tend to deal with monolithic, globally-specified models. This tutorial paper concentrates on Petri Nets with Boundaries (PNB): a compositional, graphical algebra of 1-safe nets, and its applications to reachability checking within the tool Penrose. The algorithms feature the use of compositionality and process equivalence, a powerful combination that can be harnessed to improve the performance of checking reachability and coverability in several common examples where Petri nets model realistic concurrent systems.