Stochastic and Real Time in Process Algebra: A Conceptual Overview

It is widely recognized that dealing with time related aspects in process algebra is often crucial for the specification and analysis of complex real systems. Research work in this field has led to a rather huge literature, where several kinds of time have been taken into account: time may be either based on a discrete or continuous domain, time elapsing may be either probabilistically (so-called stochastic-time) or deterministically (so-called real-time) bounded. In this paper we perform a conceptual dissertation about the treatment of the various kinds of time in transition systems where notions of composition are defined (as e.g. by defining a process algebra). We discuss general problems which are independent from the kind of time considered (concerning, e.g., the usual assumption of maximal progress of actions over time). Moreover, we show the conceptual relationship between the notion of time considered and the kind of semantics (in the sense of classical process algebra literature) which must be adopted for representing such a notion of time in the composition operators.