On the expressiveness and decidability of higher-order process calculi

Ivan Lanese, Jorge A. Pérez, Davide Sangiorgi, Alan Schmitt
2011 Information and Computation  
In higher-order process calculi the values exchanged in communications may contain processes. A core calculus of higher-order concurrency is studied; it has only the operators necessary to express higher-order communications: input prefix, process output, and parallel composition. By exhibiting a nearly deterministic encoding of Minsky machines, the calculus is shown to be Turing complete and therefore its termination problem is undecidable. Strong bisimilarity, however, is shown to be
more » ... . Further, the main forms of strong bisimilarity for higher-order processes (higher-order bisimilarity, context bisimilarity, normal bisimilarity, barbed congruence) coincide. They also coincide with their asynchronous versions. A sound and complete axiomatization of bisimilarity is given. Finally, bisimilarity is shown to become undecidable if at least four static (i.e., top-level) restrictions are added to the calculus.
doi:10.1016/j.ic.2010.10.001 fatcat:m2cam7szyzac7hd7hxwbd6a6mi