Lecture Notes in Computer Science 3472

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21 Finite State Machines 613 • λ(s, a) =λ(t, a) for each input symbol a ∈ I ,and • δ(s, a) andδ(t, a) are in the same block. It is straight-forward to check that s and t are in the same block if and only if they are equivalent. The straight-forward solution to finding this coarsest partition is to start with an initial partition of S, where two states s and t are in the same block if and only if λ(s, a) =λ(t, a) for each input symbol a ∈ I . Thereafter, this initial partition is repeatedly refined by the following method. Take a block Bi of the current partition. Examine δ(s, a) foreachs∈Biand a ∈ I . Partition Bi so that s and t are in the same block if and only if δ(s, a) andδ(t, a) areinthe same block of the current partition. The process is is iterated until no further refinements are possible. This process yields a quadratic algorithm, since each refinement requires linear time, and there can be at most |S| refinements. A more efficient algorithm has been developed by Hopcroft ([Hop71] and [AHU74, Sec. 4.13]). 21.3 Initial and Current State Uncertainty Chapters 1 – 4 use some basic definitions of the conclusions that can be made from observations of a machine’s response to input strings. The initial state uncertainty describes what we know about the initial state after applying an input string and observing the resulting output string. Definition 21.2. The initial state uncertainty after applying input sequence x ∈ I ∗ is a partition π(x ) def = {B1, B2,...,Br } of S, such that two states s, t are in the same block Bi if and only if λ(s, x )=λ(t, x ). In other words, each block in the initial state uncertainty π(x ) is the set of states from which a particular output sequence is produced in response to the input sequence x . The current state uncertainty describes what we know about the current (final) state after having applied an input string and observed the resulting output string. Definition 21.3. The current state uncertainty after applying input sequence x ∈ I ∗ is the set of subsets σ(x ) def = {δ(Bi, x ):Bi ∈ π(x )} of S. In other words, each block in the current state uncertainty σ(x )isthesetofstates that the machine can end up in after generating a particular output sequence in response to the input sequence x . While the initial state uncertainty is a partition, the current state uncertainty does not need to be a partition, but just a set of nonempty blocks 21.4 Distinguishing Experiments Chapters 1 – 4 present algorithms that investigate the structure and current state of a Mealy machine by performing experiments, i.e., applying a sequence
614 Bengt Jonsson of input symbols and observing the resulting output. An experiment can be either preset or adaptive. Apreset experiment (or preset sequence) is a fixed input sequence x ∈ I ∗ , and we are interested in observing the output sequence produced by the machine in response to x .Inanadaptive experiment (or adaptive sequence), each symbol in the input sequence depends on the output produced in response to the previous input symbols. An adaptive experiment can be formalized as a decision tree, in which the internal nodes are labeled with input symbols, and the edges are labeled with output symbols, such that edges emanating from a common node have distinct output symbols. Each leaf of an adaptive experiment can be labeled with a suitable defined outcome of the experiment for the particular case that the experiment ends up in this leaf.
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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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19 Model Checking Therese Berg 1 an
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Page 587 and 588: 19 Model Checking 597 Assistant 4.
Page 589 and 590: 19 Model Checking 599 have created
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Page 597 and 598: 20 Model-Based Testing - A Glossary
Page 599: 612 Bengt Jonsson a/0 b/0 b/1 s2 s4
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,
Page 641 and 642: 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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