A truly concurrent semantics for a process algebra using resource pomsets

  • Gastin P
  • Mislove M
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Abstract

In this paper we study a process algebra whose semantics is based on true concurrency. In our model, actions are defined in terms of the resources they need to execute, which allows a simple definition of a weak sequential composition operator. This operator allows actions which do not share any resources to execute concurrently, while dependent actions have to occur sequentially. This weak sequential composition operator may be used to automatically parallelize a sequential process. We add the customary (strict) sequential composition and a parallel composition operator allowing synchronization on specified actions. Our language also supports a hiding operator that allows the hiding of actions and even of individual resources used by actions. Strict sequential composition and hiding require that we generalize from the realm of Mazurkiewicz traces to that of pomsets, since these operations introduce “over-synchronized” traces—ones for which a pair of independent actions may occur sequentially. Our language also supports recursion and our semantics makes the unwinding of recursion visible by the use of special resources used to label unwindings. This is done on purpose in order to make divergence observable, but the usual semantics that does not observe unwindings can be obtained by using the hiding operator to abstract away from these special resources. We give both an SOS-style operational semantics for our language, as well as a denotational semantics based on resource pomsets. Generalizing results from our earlier work in this area, we derive a congruence theorem for our language which shows that the SOS-style operational rules induce the same equivalence relation on the language as the denotational semantic map does. A corollary is that our denotational model is both adequate and fully abstract relative to the behavior function defined from our operational semantics. This behavior consists naturally of the strings of actions the process can perform. This work continues our study into modelling concurrency in the absence of nondeterminism. In particular, our language is deterministic. [Copyright &y& Elsevier]

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Gastin, P., & Mislove, M. (2002). A truly concurrent semantics for a process algebra using resource pomsets. Theoretical Computer Science, 281(1–2), 369–421. https://doi.org/10.1016/s0304-3975(02)00021-x

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