In this paper we present the theory of Timed Modal Speci cations (TMS) together with its implementation, the tool Epsilon. TMS and Epsilon are timed extensions of respectively Modal Specications Lar90, LT88] and the Tav system GLZ89, BLS92]. The theory of TMS is an extension of real{timed process calculi with the speci c aim of allowing loose or partial speci cations. Looseness of speci cations allows implementation details to be left out, thus allowing several and varying implementations. We achieve looseness of speci cations by introducing two modalities to transitions of speci cations: a may and a must modality. This allows us to de ne a notion of re nement, generalizing in a natural way the classical notion of bisimulation. Intuitively, the more must{transitions and the fewer may{transitions a speci cation has, the ner it is. Also, we introduce notions of re nements abstracting from time and/or internal computation. TMS speci cations may be combined with respect to the constructs of the real{time calculus Wan90]. \Time{sensitive" notions of re nements that are preserved by these constructs are de ned 1 , thus enabling compositional veri cation. Epsilon provides automatic tools for verifying re nements. We apply Epsilon to a compositional veri cation of a train crossing example.
A timed extension of modal specifications appeared in REF in a process algebra style.
Timed Modal Specification -- Theory and Tools
IN PROC. OF THE 5TH INT. CONF. ON COMPUTER AIDED VERIFICATION, VOLUME 697 OF LECTURE NOTES IN COMPUTER SCIENCE (LNCS
Computer Science