We investigate a principled extension of the π-calculus for formal modeling of mobile communicating systems with stateful channels. In our proposed extension, called πZ, a channel is associated with a stateful abstract type in the Z specification language. We develop both reduction as well as labeled transition semantics for πZ. We show that the important properties of the π-calculus are preserved in πZ: (1) τ-transitions match reductions; and (2) bisimilarity induced by the labeled transitions is closed under parallel composition, name restriction, and a restricted recursion. The paper illustrates the use of stateful channels by modeling the ‘hidden node problem’ in a wireless network.
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Jayaraj Poroor and Bharat Jayaraman, “Modeling mobile stateful channels in πZ”, Science of Computer Programming, vol. 78, pp. 1470 - 1489, 2013.