Lecture Notes in Computer Science 3472

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330 Levi Lúcio and Marko Samer 1 2 3 4 ✎ ☞ Modulo ✍ ✌ ✟ ✟ ❍ ❍❍❍ ✟ ✟ b? k � � ❅ ❅ � � ❅ ❅ = m? > m? mod2 = 0 mod2 = 1 � � � � � � Fig. 12.1. Classification-tree of Modulo ever, new disjuncts maybe introduced. This can be corrected by post-processing the disjuncts after the elimination step. As already mentioned, each of the disjuncts obtained by this procedure represents a test case. Thus, the disjuncts can be separated into schemas for each test case with the same declaration part as the original schema and one of the disjuncts as predicate part respectively. Case studies by Helke et al. [HNS97] have shown that most of the generated test cases after the first step are not satisfiable. Therefore, the second step, i.e., the simplification by removing unsatisfiable disjuncts and reducing redundancy, is the most expensive part in this approach. The Classification-Tree Method. The drawback of such purely syntaxoriented approaches as proposed by Helke et al. [HNS97] is that the user has only little influence on the generation of relevant test cases. Therefore, a combination with the semantic-oriented approach of classification-trees [GG93] was investigated by Singh et al. and Sadeghipour [SCS97, Sad98]. In the classification-tree method, the test object is analyzed with respect to properties which are considered to be relevant for the test. For each such property, a disjoint partitioning is performed. The partitions can then be further classified until a sufficiently refined partitioning is reached. It is easy to see that this refinement process can be graphically represented as a tree, the classification-tree. For instance, the classification-tree of the schema Modulo in Sec. 12.2.1 concerning the variables b? andk is shown in Fig. 12.1. In this tree, b? is partitioned depending on being equal to or greater than m?, and k is partitioned depending on being even or odd. Each combination of the leaves of different classifications in such a tree represents a high-level test case. In our example, each row in the combination table below the classification-tree represents such a high-level test case (according to the marked points in the table). Since these test cases contain only variables occurring in the classificationtree, we have to add them as additional predicate to the original schema in order to obtain complete test cases. For instance, if we add the fourth test case � �
12 Technology of Test-Case Generation 331 (b? > m?) ∧ (k mod 2 = 1) to the predicate part of the original schema, we obtain after some simplifications the complete test case schema: Modulo (Partition4) b?, m?, r! :N b? > m? (r! < m?) ∨ (m? =0) ∃ k : N • (k mod 2 = 1) ∧ (b? =m? ∗ k + r!) This test case can be further refined by transforming it into disjunctive normal form as in the previous approach, which yields two refined test cases: (b? > m?) ∧ (r! < m?) ∧∃k : N • ((k mod 2 = 1) ∧ (b? =m? ∗ k + r!)) (b? > m?) ∧ (m? =0)∧∃k : N • ((k mod 2 = 1) ∧ (b? =m? ∗ k + r!)) Note that in addition to the semantic aspects, the classification-tree method provides a hierarchical structuring of the test cases, while test cases in the pure disjunctive normal form approach are completely unstructured. An application of theorem proving to support this approach was presented by Sadeghipour [Sad98]. In particular, the theorem prover Isabelle [Pau94, NPW02] is used as integral part of a tool environment for test case generation based on the classificationtree method. The theorem prover is applied, e.g., for simplification tasks, for checking test data consistency, and for test evaluation. Partitioning Heuristics. An approach with the objective of building a uniform theoretical foundation and generalizing the above methods was presented by Burton et al. [BCM00, Bur00, Bur02]. This approach is based on CADiZ [TM95, Toy96, Toy98], a Z type checker and theorem prover. Since the input language of CADiZ is Z itself, there is no necessity for translating Z specifications. The main difference to the approaches of Helke et al. [HNS97], Singh et al., and Sadeghipour [SCS97, Sad98] is that various partitioning heuristics are supported in the work of Burton et al. [BCM00, Bur00, Bur02]. In particular, the test case generation of Helke et al. [HNS97] is based on disjunctive normal form partitioning as shown above. This partitioning, however, can be generalized by other partitioning heuristics such as heuristics based on boundary value analysis or type analysis. For instance, the predicate m ≥ 0canbe partitioned by boundary value analysis into (m =0)∨ (m =1)∨ (m > 1), and the domain of the variable n ∈ Z can be partitioned by type analysis into (n < 0) ∨ (n =0)∨ (n > 0). In addition, the partitioning can also be based on fault-based heuristics which take the experience of faults detected in previous builds into account. For instance, if the specified operation n 2 is assumed to be incorrectly implemented as 2 ∗ n, wheren ∈ N, then the partitioning would be (n =1)∨ (n > 2) because n 2 and 2 ∗ n cannot be distinguished by n =0andn =2. Of course, these partitionings can also be performed by the classification-tree method of Singh et al. and Sadeghipour [SCS97, Sad98]. However, as we will see
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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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Page 277 and 278: Part III. Model-Based Test Case Gen
Page 279 and 280: 282 Alexander Pretschner and Jan Ph
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13 Real-Time and Hybrid Systems Tes
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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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13 Real-Time and Hybrid Systems Tes
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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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19 Model Checking 559 The first sta
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19 Model Checking 561 function I :
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coffee coin tea 19 Model Checking 5
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AX (φ) :=¬EX (¬φ) AF (φ) :=Atr
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19 Model Checking 567 Another appro
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19 Model Checking 569 has a transit
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19 Model Checking 571 The alternati
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19 Model Checking 573 Obviously the
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19 Model Checking 575 purposes ther
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19 Model Checking 577 otherwise it
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19 Model Checking 579 Expanding a P
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19 Model Checking 581 We conduct an
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• SA ⊆ Σ ∗ is a nonempty fin
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19 Model Checking 585 When OT is cl
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19 Model Checking 587 • se = s
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19 Model Checking 589 the new colum
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19 Model Checking 591 Henceforth th
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19 Model Checking 593 DT , the tran
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19 Model Checking 595 queries. At t
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19 Model Checking 597 Assistant 4.
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19 Model Checking 599 have created
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19 Model Checking 601 Logic (see Se
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19 Model Checking 603 linear time l
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20 Model-Based Testing - A Glossary
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20 Model-Based Testing - A Glossary
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612 Bengt Jonsson a/0 b/0 b/1 s2 s4
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614 Bengt Jonsson of input symbols
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616 Joost-Pieter Katoen The followi
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618 Literature [AFH94] Rajeev Alur,
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620 Literature [BCMD90] J. R. Burch
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622 Literature [BRV95] Ed Brinksma,
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624 Literature [CL97a] Duncan Clark
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626 Literature [DGNP04] Z. R. Dai,
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628 Literature [FHP02] Eitan Farchi
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630 Literature [GL02] Hubert Garave
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632 Literature [Hib61] Thomas N. Hi
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634 Literature [HR01b] Klaus Havelu
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636 Literature [KKL + 01] M. Kim, S
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638 Literature [LPY97] Kim Guldstra
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640 Literature [Müh97] H. Mühlenb
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642 Literature [Pha93] M. Phalippou
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644 Literature [RdBJ00] V. Rusu, L.
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646 Literature [Sch00] Johann M. Sc
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648 Literature [SVG02] S. Schulz an
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650 Literature [Vas73] M. P. Vasile
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Index =⇒ , 175 ioco, 187 ioconf,
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homing sequence, 8 - adaptive, 8, 2
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eset sequence, see synchronizing se
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timed transition system, 223, 360,
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