Abstract
There has been considerable controversy in concurrency theory between the ‘interleaving’ and ‘true concurrency’ schools. The former school advocates associating a transition system with a process which captures concurrent execution via the interleaving of occurrences: the latter adopts more complex semantic structures to avoid reducing concurrency to interleaving.
In this paper we show that the two approaches are not irreconcilable. We define a timed process algebra where occurrences are associated with intervals of time, and give it a transition system semantics. This semantics has many of the advantages of the interleaving approach; the algebra admits an expansion theorem, and bisimulation semantics can be used as usual. Our transition systems, however, incorporate timing information, and this enables us to express concurrency: merely adding timing appropriately generalises transition systems to asynchronous transition systems, showing that time gives a link between true concurrency and interleaving. Moreover, we can provide a complete axiomatisation of bisimulation for our algebra; a result that is often problematic in a timed setting.
Another advantage of incorporating timing information into the calculus is that it allows a particularly simple definition of action refinement; this we present.
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Aceto, L., Murphy, D. (1993). On the ill-timed but well-caused. In: Best, E. (eds) CONCUR'93. CONCUR 1993. Lecture Notes in Computer Science, vol 715. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57208-2_8
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DOI: https://doi.org/10.1007/3-540-57208-2_8
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