By Kerry Urbaniak
Booklet by means of Urbaniak, Kerry
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Additional resources for Microprocessors: Experiments for the Motorola 6800
3, num. 1, 1–61, 2007. , “Is your model checker on time? On the complexity of model checking for timed modal logics”, Journal of Logic and Algebraic Programming, vol. 52–53, 7–51, 2002. , “A framework for scheduler synthesis”, 20th IEEE Real-Time Systems Symposium (RTSS’99), pp. 154–163, Phoenix, AZ, USA, IEEE Computer Society Press, December 1999. , “A methodology for the construction of scheduled systems”, 6th International Symposium on Formal Techniques in Real-Time and Fault-Tolerant Systems (FTRTFT’00), vol.
A formula of LTL is interpreted at position i of an (inﬁnite) run starting from the initial state σ : q0 − → q1 − → q2 · · · . For i ≥ 0, we simply write σ(i) for the ith state of Timed Model-Checking 47 σ (here qi ). The semantics of LTL is then inductively deﬁned by σ, i |= P, σ, i |= ¬ϕ σ, i |= ϕ ∧ ψ, σ, i |= Xϕ σ, i |= ϕUψ, if P is in the set (σ(i)) of labels of q ; if σ, i does not satisfy ϕ ; if q satisﬁes both ϕ and ψ ; if σ, i + 1 |= ϕ ; if there exists j ≥ i such that σ, j |= ψ and for all k, i ≤ k < j, σ, k |= ϕ.
In untimed case, two fragments of CTL* [CLA 86] are frequently used: linear temporal logic (LTL), for linear time [PNU 77]) and computation tree logic (CTL), for branching time [CLA 81, EME 82]). We recall the deﬁnition of these logics and explain how they are extended with quantitative constraints. 1. Temporal logics CTL and LTL Let us consider again that Prop be a set of atomic propositions. The formule of LTL approach are deﬁned by the grammar ϕ, ψ ::= P | ¬ϕ | ϕ ∧ ψ | Xϕ | ϕUψ, where P ∈ Prop.