A Formal Definition of Time in LOTOS

Abstract.

Enhanced Timed-LOTOS, denoted ET-LOTOS, is an extension of LOTOS that allows the modelling of real-time behaviours. It covers all the aspects of full LOTOS, including data types, it supports both a dense and a discrete time domain and can manipulate time values as any other data values. A tutorial on ET-LOTOS, showing many application examples, has already been published [LéL97]. The present paper adds to it by providing an in-depth presentation of its theoretical aspects. The complete semantics is given and explained, and its properties are studied. In particular, we prove that the semantics is consistent and that strong bisimulation is a congruence. This requires to deal carefully with the presence of negative premises in the operational semantics, which are necessary to express urgency. ET-LOTOS is also shown to be a conservative extension of LOTOS for guarded processes, and is the basis of the timed extension of LOTOS currently developed by ISO [ISO98]. To our knowledge, this is the first in-depth study of a language that combines data types and real-time behaviours.