On decidability properties of two fragments of the asynchronous π-calculus.
Aranda Bueno, Jesús Alexander | 2014-03-28
In (Cacciagrano, et al., 2008) the authors studied the expressiveness of persistence in the asynchronous π-calculus,
henceforth Aπ. They considered Aπ and three sub-languages of it, each capturing one source of persistence: the
persistent-input calculus (PIAπ), the persistent-output calculus (POAπ), and the persistent calculus (PAπ). They
prove that, under some general conditions, there cannot be an encoding from Aπ into a (semi)-persistent calculus
preserving the must-testing semantics, a semantics sensitive to divergence.
In this paper we support and strengthen the separation results of (Cacciagrano, et al., 2008) by showing that
convergence and divergence are two decidable properties in a fragment of POAπ and PAπ, in contrast to what happen
in Aπ. Thus, it is shown that there cannot be a (computable) encoding from Aπ into PAπ and in such a fragment of
POAπ, preserving divergence or convergence. These impossibility results don’t presuppose any condition on the
encodings and involve directly convergence for first time in the study of the expressiveness of persistence of .