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The majority of modern systems exhibit sophisticated concurrent behaviour, where several system components modify and observe the system state with fine-grained atomicity. Many systems (e.g., multi-core processors, real-time controllers) also exhibit truly concurrent behaviour, where multiple events can occur simultaneously. This paper presents data refinement defined in terms of an interval-based framework, which includes high-level operators that capture non-deterministic expression evaluation. By modifying the type of an interval, our theory may be specialised to cover data refinement of both discrete and continuous systems. We present an interval-based encoding of forward simulation, then prove that our forward simulation rule is sound with respect to our data refinement definition. A number of rules for decomposing forward simulation proofs over both sequential and parallel composition are developed.
We give a formalization of Pratts intuitive sculpting process for higher-dimensional automata (HDA). Intuitively, an HDA is a sculpture if it can be embedded in (i.e., sculpted from) a single higher dimensional cell (hypercube). A first important res
Sesqui-pushout (SqPO) rewriting along non-linear rules and for monic matches is well-known to permit the modeling of fusing and cloning of vertices and edges, yet to date, no construction of a suitable concurrency theorem was available. The lack of s
We develop local reasoning techniques for message passing concurrent programs based on ideas from separation logics and resource usage analysis. We extend processes with permission- resources and define a reduction semantics for this extended languag
We view channels as the main form of resources in a message-passing programming paradigm. These channels need to be carefully managed in settings where resources are scarce. To study this problem, we extend the pi-calculus with primitives for channel
We define a pi-calculus variant with a costed semantics where channels are treated as resources that must explicitly be allocated before they are used and can be deallocated when no longer required. We use a substructural type system tracking permiss