Compositional specification and reachability checking of net systems

Abstract

Concurrent systems are frequently scrutinised using automated model checking, routinely using Petri nets as a model. While for small system models, it is often sufficient to give the system specification in a monolithic manner, for larger systems this approach is infeasible. Instead, a compositional, or component-wise specification can be used. However, while existing model checking techniques sometimes allow the specification of nets in terms of components, the techniques used for checking properties of the system all consider the composed, global net.

In this thesis, we investigate and advocate compositional system specification and an alternative approach to model checking that uses the structural compositional information
to its advantage, vastly improving efficiency in many examples. In particular, we examine the categorical structure of component nets and their semantics, illustrating the functoriality of a map between the categories as compositionality. We introduce contextual Petri Nets with Boundaries (PNBs), adding read arcs, which naturally model behaviour that non-destructively reads the token state of a place. Furthermore, we introduce a type-checked specification language that allows us to compositionally construct systems to be modelled using PNBs, whilst ensuring that only correct compositions
are expressible. We then discuss and implement compositional statespace generation, which can be used to check reachability. Via optimisations using weak language equivalence and memoisation, we obtain substantial speed ups and demonstrate that our checker outperforms the current state-of-the-art for several examples. A final contribution is the compositional specification of existing benchmark examples, in more natural, component-wise style.

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