Absolute versus Relative Time in Process Algebras

Abstract

Timed process algebras are useful tools for the specification and verification of real-time systems. We study the relationships between two of these algebras, $\text{c}$I$\text{pa}$ (closed interval process Algebra) and TCCS (temporal CCS), which deal with temporal aspects of concurrent systems by following very different interpretations: durational actions versus durationless actions, absolute time versus relative time, timed functional behavior versus time and functional behavior, local clocks versus global clocks. We show that these different choices are not irreconcilable by presenting simple mappings from $\text{c}$I$\text{pa}$ to TCCS which preserve the behavioral equivalences over the two timed calculi. These results hold whenever basic actions are interpreted as either eager or lazy, whenever the starting time of action execution is observed rather than their completion time. A study on the size of the labelled transition systems describing the transitional semantics of cIpa processes and those describing the transitional semantics of their translated versions is also presented.