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Lecture Notes in Computer Science 3472

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8 Test Derivation from Timed Automata 219<br />

applied to A start<strong>in</strong>g from any state s of its OS(A ). The application of σ to<br />

A <strong>in</strong> s uniquely determ<strong>in</strong>es a f<strong>in</strong>ite, maximal execution fragment <strong>in</strong> OS(A ).<br />

How to perform a test sequence is shown <strong>in</strong> the follow<strong>in</strong>g def<strong>in</strong>ition. The<br />

outcome of perform<strong>in</strong>g a test sequence on A is described <strong>in</strong> terms of an auxiliary<br />

labeled transition system T .<br />

Def<strong>in</strong>ition 8.27. The test sequence is the LTS T = 〈(Exp × Q),Σ,(ɛ, s0), ↠〉<br />

with (Exp ×Q) as its set of states, where Exp is the test sequence to be executed,<br />

Σ is a set of actions, (ɛ, s0) is (arbitrarily chosen) <strong>in</strong>itial state, and a transition<br />

relation ↠ that is <strong>in</strong>ductively def<strong>in</strong>ed as the least relation satisfy<strong>in</strong>g the follow<strong>in</strong>g<br />

four rules, for all q, q ′ ∈ Q,σ ∈ Exp, i ∈I, o ∈Oand d, d ′ ∈ R >0 :<br />

•<br />

•<br />

•<br />

•<br />

q o!<br />

↣ q ′<br />

(σ,q) o!<br />

↠ (σ,q ′ )<br />

q i?<br />

↣ q ′<br />

(i?σ,q) i?<br />

↠ (σ,q ′ )<br />

q d<br />

↣ q ′<br />

(dσ,q) d<br />

↠ (σ,q ′ )<br />

q d′<br />

↣ q ′ , sup{t∈R >0 |q t<br />

↣}=d ′

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