Responsive Choice in Mobile Processes

In the π-calculus [MPW92], activeness is the ability to get in contact with a process through a particular channel, and responsiveness is the ability to conduct a conversation, or session, through that channel. The latter is of course strongly dependent on the type of the channel. These have been widely studied concepts, dating back from Sangiorgi’s receptiveness [San99], and closely related to Acciai and Boreale’s responsiveness [AB08] or Kobayashi’s livelock freedom [Kob02]. A common approach is to ensure there are no livelocks by assigning levels to name occurrences, effectively calculating in which order they become active. We are particularly interested in conditional activeness, specifically in statements such as γ / ε, where γ and ε are logical statements on channel activeness, and the whole meaning “γ holds provided ε is made available (e.g. through parallel composition)”. In terms of levels this could be thought as an inequality whose unknowns are the channel levels. This permits analysing several components of a system individually, and then predict the behaviour of the whole by composing the components’ types.