By Nicolas Navet, Stephan Merz

This name is dedicated to offering the most vital recommendations and strategies for describing real-time structures and studying their habit to be able to let the dressmaker to accomplish promises of temporal correctness.Topics addressed comprise mathematical types of real-time platforms and linked formal verification recommendations resembling version checking, probabilistic modeling and verification, programming and outline languages, and validation techniques according to trying out. With contributions from authors who're specialists of their respective fields, it will give you the reader with the cutting-edge in formal verification of real-time platforms and an outline of obtainable software program instruments.

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**Example text**

The trace trace(ρ) of an execution ρ is the projection of ρ on the set Λ! ∪ Λ? of observable actions. The set of traces of an IOSTS S is the set of all traces of all executions of S, and is denoted by Traces(S). Let F ⊆ L be a set of locations of an IOSTS S. An execution ρ of S is recognized by F if the execution terminates in a state in F × V. A trace is recognized by F if it is the trace of an execution recognized by F . The set of traces of an IOSTS S recognized by a set F of locations is denoted by Traces(S, F ).

The traditional state class graph construction (SCG) has been used in many works, academic and industrial, concerning hardware or software, and has been integrated into many tools. All the techniques discussed in this chapter are supported by the Tina environment [BER 04]. Once a ﬁnite representation of the set of states is available, we can apply to it model checking techniques to prove properties of the state space. These possibilities were illustrated in the framework of temporal logic LT L.

BER 03b] Let c = (m, Q = {Gγ g}) and c = (m , Q = {G γ g }). If all transitions enabled at m or m have bounded static ﬁring intervals, then: c ≡ c ⇔ m = m ∧ Sol(Q) = Sol(Q ) The general case will be discussed later. Note that when a transition k is ﬁrable at any date beyond its earliest ﬁring time e, all clock vectors whose component k is at least equal to e, and differing only by this component, describe the same state. 2. Construction of the SSCG Strong state classes are represented by pairs (m, Q), where m is a marking and Q a clock domain described by a system of linear inequalities Gγ g.