Lecture Notes in Computer Science 3472

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600 Therese Berg and Harald Raffelt VC-counterexample No counterexample Check equivalence (VC algorithm) Report no error found Incremental Learning (Angluin) Model Checking wrt. current model Counterexample found Compare counterexample with system Conformance established Counterexample confirmed Report counterexample Counterexample Fig. 19.15. Overview of the Adaptive Model Checking Algorithm. (1) If the model checker finds a mc-counterexample for the checked property, the SUT runs the counterexample in order to see if it is indeed a sequence of actions that can be performed by the SUT. • If the SUT accepts the mc-counterexample we have an input sequence that shows that the SUT does not satisfy the property. Then the mccounterexample is reported and the AMC algorithm terminates. • In the second scenario where the sequence can not be performed by the SUT, the mc-counterexample will be given to the learning algorithm and the model will be refined. (2) In the second case, if the model checker does not produce a mc-counterexample, one has to investigate whether the model corresponds to the SUT. Applying the VC algorithm resolves this question. As before, if a vc-counterexample is found, the counterexample is given to Angluin’s algorithm and the model is refined. If no vc-counterexample is found the AMC algorithm concludes that the SUT satisfies the property and the AMC algorithm terminates. We will now present the AMC algorithm in more detail. Model The model of the SUT is constructed by Angluin’s algorithm in the AMC method. The AMC method assumes that the SUT gives information whether an input can be currently executed by the SUT. Therefore the language of the SUT is assumed to be prefix-closed and hence the model as well. The model is a finite automaton and its runs represent only the successful experiments (strings) in the SUT. The learning algorithm used in AMC to learn this model is Angluin’s algorithm. We assume that we know an upper bound on the number of states, n, of the SUT. Property The property is given as an LTL formula, and this can be translated into a Büchi automaton. So the property can be expressed in Linear Temporal
19 Model Checking 601 Logic (see Section 19.3.2 on Linear Temporal Logic) and transformed into a finite automaton A¬φ on infinite words not accepting the property, usually a Büchi automaton. The algorithm for model checking LTL is presented in detail in Section 19.3.3. LTL is used since it delivers counterexamples in the format of a sequence of actions. Since Computational Tree Logic is not suitable to describe properties of regular languages and counterexamples in CTL are not just words of a language, CTL cannot be used in the AMC algorithm. Initialization Let M be the SUT and Ainit an initial model of M in the following section. The AMC algorithm is initialized by providing Angluin’s algorithm with the information of the initial model so that fewer calls to the (time expensive) VC algorithm are needed. In [GPY02], three ways to use the initial model are proposed. (1) A false negative mc-counterexample t found (i.e., a sequence t that was considered to be a counterexample, but has turned out not to be an actual execution of the SUT M). This corresponds to a counterexample in Angluin’s algorithm. Following Angluin’s algorithm we perform membership queries for all prefixes of t. (2) The runs T of a spanning tree of the model Ainit as the initial set of row labels SA (access strings). We initialize Angluin’s algorithm by adding each s ∈ SA to OT and perform membership queries for the missing entries. (3) A set of separating sequences DS(Ainit ), see Section 4.4, calculated for the states of Ainit as the initial set of column labels EA. Thus, we initialize Angluin’s algorithm by setting OT to be empty, and EA = DS(Ainit ). So this three ways of initializing the sets SA and EA account for the attempt to speed up learning, but with the entries in OT queried for on the SUT at hand now. Note that when using all three initializations and if Ainit models M accurately with these choices of SA and EA then this will allow Angluin’s algorithm to learn Ainit correctly, without the assistance of the expensive equivalence check (VC algorithm). Handling Model-Checking Counterexamples The model checker can construct two types of mc-counterexamples to a LTL formula, finite and infinite. In the first case there is no extra work in handling it: The counterexample is given directly to Angluin’s algorithm. In the second case we must make the counterexample finite in order for Angluin’s algorithm to use it. An infinite counterexample is an ultimately periodic word of the form w1w ω 2 where w1, w ω 2 ∈ Σ∗ . Assuming that the automaton being checked has n number of states, the counterexample given to Angluin’s algorithm is w1w n+1 2 . Running w1 in A¬φ it needs to terminate in an accepting state s. Starting from s the second part w2 needs to terminate in s as well. For each such pair, we apply the second part n more times. That is, we try to run the string w1w n+1 2 .Ifwe succeed, this means that there is a cycle in A¬φ ∩M through a state with s
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Lecture Notes in Computer Science 3
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Volume Editors Manfred Broy Martin
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VI Preface The last part of the boo
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VIII Contents 13 Real-Time and Hybr
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2 Part I. Testing of Finite State M
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1 Homing and Synchronizing Sequence
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s2 a/1 1 Homing and Synchronizing S
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1.3.2 Computing Synchronizing Seque
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A1 A2 Bad 1 Homing and Synchronizin
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36 Moez Krichen b/1 a/0 s1 b/1 a/1
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38 Moez Krichen Now, even for minim
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40 Moez Krichen the algorithms for
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42 Moez Krichen ∀ s, s ′ ∈ S
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44 Moez Krichen In this proposition
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46 Moez Krichen Proposition 2.6. If
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48 Moez Krichen Algorithm 5 Checkin
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50 Moez Krichen (5) Edges emanating
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52 Moez Krichen graph of this machi
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54 Moez Krichen v12 v6 v11 1 I = {s
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56 Moez Krichen B of π, a is a-val
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58 Moez Krichen I = {s1, s2, s3, s4
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60 Moez Krichen Definition 2.19. A
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62 Moez Krichen Algorithm 7 Computi
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64 Moez Krichen Algorithm 8 Computi
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66 Moez Krichen The two authors als
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3 State Verification Henrik Björkl
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a/1 s1 s3 b/1 a/1 b/1 a/0 s2 s4 3 S
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3 State Verification 73 Thus (s, Q)
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3 State Verification 75 0, and x ca
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s1 s3 a/0 b/0 a/1 s2 s4 3 State Ver
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3.4.2 Naik’s Algorithm 3 State Ve
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s1 s2 s3 s1 s3 s3 a/0 a/0 s1 s2 s3
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3 State Verification 83 Since the m
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3 State Verification 85 x = a1a2 ..
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4 Conformance Testing Angelo Gargan
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4 Conformance Testing 89 the test u
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4 Conformance Testing 91 state. For
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4 Conformance Testing 93 This check
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s1 s1 a b s2 s2 a b s3 4 Conformanc
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4 Conformance Testing 97 Using a Q
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4 Conformance Testing 99 this case
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4.4.5 Cost and Length 4 Conformance
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t τ (t,si−1) x τti−1 ,si si
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si 1 2 w1 t i w 2 3 a: in MS si 1 w
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4 Conformance Testing 107 ti = δ(s
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4 Conformance Testing 109 Example.
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4 Conformance Testing 111 • If on
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114 Part II. Testing of Labeled Tra
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5 Preorder Relations ∗ Stefan D.
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5 Preorder Relations 119 power of r
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5 Preorder Relations 121 To summari
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5 Preorder Relations 123 Two import
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∧ ⊥⊤ ⊥ ⊥⊥ ⊤ ⊥⊤
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5 Preorder Relations 127 Definition
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5 Preorder Relations 129 For one th
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5 Preorder Relations 131 We close t
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s a b t 5 Preorder Relations 133 y
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5 Preorder Relations 135 (1) p ⊑m
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a p ′ τ b p ′′ τ τ a a b 5
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5 Preorder Relations 139 It should
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coin coin e c coin coin τ 5 Preord
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5 Preorder Relations 143 for free.
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5 Preorder Relations 145 condition
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5 Preorder Relations 147 ⊑←→
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5 Preorder Relations 149 The utilit
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152 Valéry Tschaen The labels repr
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154 Valéry Tschaen Intuitively, th
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156 Valéry Tschaen Definition 6.2.
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158 Valéry Tschaen By this theorem
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160 Valéry Tschaen The test suite
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162 Valéry Tschaen each sequence (
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164 Valéry Tschaen and B2 are LOTO
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166 Valéry Tschaen 6.4.2 The CO-OP
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168 Valéry Tschaen a τ q0 τ τ q
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170 Valéry Tschaen Concerning the
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7 I/O-automata Based Testing Machie
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7 I/O-automata Based Testing 175 th
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7 I/O-automata Based Testing 177 in
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7 I/O-automata Based Testing 179 sp
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7 I/O-automata Based Testing 181 na
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7 I/O-automata Based Testing 183 Un
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7 I/O-automata Based Testing 185 We
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7 I/O-automata Based Testing 187 fa
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7 I/O-automata Based Testing 189 Th
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7 I/O-automata Based Testing 191 Ac
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7 I/O-automata Based Testing 193 vi
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7 I/O-automata Based Testing 195 De
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7 I/O-automata Based Testing 197 To
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7 I/O-automata Based Testing 199 In
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8 Test Derivation from Timed Automa
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s0 on, true, {c} off , c =5, ∅ 8
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8.3 Testing Event Recording Automat
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[s1, z], z = con < 5, 8 Test Deriva
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Ψ(S ′ )={PE ′ | E ′ ∈ 2E(S
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{s0}, p0 p0 : tt 8 Test Derivation
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s0 c = ∞ 8 Test Derivation from T
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Example. The Light Switch can be de
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��s0� ,c=0.0 s0 en, on, {c :=
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��s0� ,c=0 s0 8 Test Derivati
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234 Verena Wolf to probabilistic tr
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236 Verena Wolf • A finite trace
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238 Verena Wolf (a, 0.2) v1 sP (a,
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240 Verena Wolf 1 2 sP a b µ λ 1
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242 Verena Wolf (a, 1 4 ) (a, 1 4 )
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244 Verena Wolf 9.6 Test Processes
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246 Verena Wolf We present two appr
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248 Verena Wolf specification proce
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250 Verena Wolf sP (τ, 1 1 ) (c, 3
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252 Verena Wolf sP (a, 1 1 ) (a, 2
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254 Verena Wolf v1 u1 w1 1 2 sP λ
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256 Verena Wolf • P ⊑ must JY Q
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258 Verena Wolf u1 s M ′ 1 (a, r1
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260 Verena Wolf Proposition 9.22. L
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262 Verena Wolf Now let Q min be th
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264 Verena Wolf (8) (⊑BC , ⊑CH
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266 Verena Wolf is that an action a
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268 Verena Wolf can perform τ-tran
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270 Verena Wolf T np,re seq ⊑ tr
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272 Verena Wolf t2 t4 a sT t1 b b t
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274 Verena Wolf model test processe
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Part III Model-Based Test Case Gene
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Part III. Model-Based Test Case Gen
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282 Alexander Pretschner and Jan Ph
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11 Evaluating Coverage Based Testin
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12 Technology of Test-Case Generati
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Increment ∆Counter 12 Technology
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(12.4) ✟ nat(X ′ ) {A/0, B/X
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a: b: (6) α1+1−α2 α2 a: b: PC:
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12.5 Summary 12 Technology of Test-
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13 Real-Time and Hybrid Systems Tes
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Test Driver SUT 13 Real-Time and Hy
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fitness 13 Real-Time and Hybrid Sys
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13.5 Summary 13 Real-Time and Hybri
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390 Part IV. Tools and Case Studies
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392 Axel Belinfante, Lars Frantzen,
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440 Wolfgang Prenninger, Mohammad E
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Part V Standardized Test Notation a
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466 George Din inter-operability te
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468 George Din • Tabular Presenta
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470 George Din 16.3.1 Test Building
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472 George Din Abstract Test System
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474 George Din field can be marked
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476 George Din • omit: the value
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478 George Din altstep Default() ru
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480 George Din alt { [] httpPort.re
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482 George Din • Test Management
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484 George Din Value Type getType()
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486 George Din This task is rather
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488 George Din hosts, of preparing
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490 George Din A B C D MEM = 256 MB
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492 George Din A hardware load moni
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494 George Din ptcType2 ptcType3
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496 George Din communicate with the
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498 Zhen Ru Dai U2TP document is no
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500 Zhen Ru Dai state machines, sta
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502 Zhen Ru Dai TestResult TestCase
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504 Zhen Ru Dai can be mapped to JU
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506 Zhen Ru Dai 17.4 Test Developme
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508 Zhen Ru Dai Slave: Master: SRI
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510 Zhen Ru Dai sa: Slave− Appli
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512 Zhen Ru Dai sdConnect_To_Master
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514 Zhen Ru Dai BluetoothUnitTest
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516 Zhen Ru Dai is returned to the
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518 Zhen Ru Dai (1) /* test configu
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520 Zhen Ru Dai (1) /* test case */
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Part VI Beyond Testing This last pa
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526 Séverine Colin and Leonardo Ma
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Page 539 and 540: 548 Séverine Colin and Leonardo Ma
Page 547 and 548: 19 Model Checking Therese Berg 1 an
Page 549 and 550: 19 Model Checking 559 The first sta
Page 551 and 552: 19 Model Checking 561 function I :
Page 553 and 554: coffee coin tea 19 Model Checking 5
Page 555 and 556: AX (φ) :=¬EX (¬φ) AF (φ) :=Atr
Page 557 and 558: 19 Model Checking 567 Another appro
Page 559 and 560: 19 Model Checking 569 has a transit
Page 561 and 562: 19 Model Checking 571 The alternati
Page 563 and 564: 19 Model Checking 573 Obviously the
Page 565 and 566: 19 Model Checking 575 purposes ther
Page 567 and 568: 19 Model Checking 577 otherwise it
Page 569 and 570: 19 Model Checking 579 Expanding a P
Page 571 and 572: 19 Model Checking 581 We conduct an
Page 573 and 574: • SA ⊆ Σ ∗ is a nonempty fin
Page 575 and 576: 19 Model Checking 585 When OT is cl
Page 577 and 578: 19 Model Checking 587 • se = s
Page 579 and 580: 19 Model Checking 589 the new colum
Page 581 and 582: 19 Model Checking 591 Henceforth th
Page 583 and 584: 19 Model Checking 593 DT , the tran
Page 585 and 586: 19 Model Checking 595 queries. At t
Page 587 and 588: 19 Model Checking 597 Assistant 4.
Page 589: 19 Model Checking 599 have created
Page 593 and 594: 19 Model Checking 603 linear time l
Page 595 and 596: 20 Model-Based Testing - A Glossary
Page 597 and 598: 20 Model-Based Testing - A Glossary
Page 599 and 600: 612 Bengt Jonsson a/0 b/0 b/1 s2 s4
Page 601 and 602: 614 Bengt Jonsson of input symbols
Page 603 and 604: 616 Joost-Pieter Katoen The followi
Page 605 and 606: 618 Literature [AFH94] Rajeev Alur,
Page 607 and 608: 620 Literature [BCMD90] J. R. Burch
Page 609 and 610: 622 Literature [BRV95] Ed Brinksma,
Page 611 and 612: 624 Literature [CL97a] Duncan Clark
Page 613 and 614: 626 Literature [DGNP04] Z. R. Dai,
Page 615 and 616: 628 Literature [FHP02] Eitan Farchi
Page 617 and 618: 630 Literature [GL02] Hubert Garave
Page 619 and 620: 632 Literature [Hib61] Thomas N. Hi
Page 621 and 622: 634 Literature [HR01b] Klaus Havelu
Page 623 and 624: 636 Literature [KKL + 01] M. Kim, S
Page 625 and 626: 638 Literature [LPY97] Kim Guldstra
Page 627 and 628: 640 Literature [Müh97] H. Mühlenb
Page 629 and 630: 642 Literature [Pha93] M. Phalippou
Page 631 and 632: 644 Literature [RdBJ00] V. Rusu, L.
Page 633 and 634: 646 Literature [Sch00] Johann M. Sc
Page 635 and 636: 648 Literature [SVG02] S. Schulz an
Page 637 and 638: 650 Literature [Vas73] M. P. Vasile
Page 639 and 640: Index =⇒ , 175 ioco, 187 ioconf,
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homing sequence, 8 - adaptive, 8, 2
Page 643 and 644:
eset sequence, see synchronizing se
Page 645:
timed transition system, 223, 360,
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