Lecture Notes in Computer Science 3472

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6 Test Generation Algorithms Based on Preorder Relations 169 The reverse transformation is: ⌊Ref (g)⌋ = {E ∩ init(g) | E ∈ Ref (g)} From LTS to RG The first step of the method consists in the construction of the refusal graph corresponding to the LTS of a specification. As for the CO-OP method, we use LOTOS notation. Definition 6.4.4 (RG associated with an LTS) The refusal graph rg(M ) associated to the LTS M =(Q, L, →, q 0) is defined by the 5-tuple (G, L,∆,Ref , g0) where: • g0 = q0 after ɛ; • (G ⊆P(Q), L,∆⊆ G×L×G) is the labeled graph rg(g0), whereforallg⊆ Q, rg(g) is recursively defined by: rg(g) = [] a∈init(g) a; rg(g after a) • for all g ∈ G, ⌊Ref (g)⌋ = Min({init(g) \ init(q) | q ∈ g}). where for E ∈P(P(L)), Min(E) =E \{X |∃Y ∈ L : X ⊆ Y and X �= Y } and for R ⊆P(P(L)), Min(R) ={Min(E) | E ∈ R}. Consider again the LTS shown in Fig. 6.7, its associated refusal graph is given in Fig. 6.10. The label of each node g is the value of ⌊Ref (g)⌋. Intuitively, the value of ⌊Ref (g0)⌋ means that, in the initial state of he specification, either a or c may be refused, but not both. g1 {{}} a g0 {{a}, {c}} b g2 {{}} c q3 {{}} Fig. 6.10. Refusal graph G Transformation of RG The second step of the method is to transform the refusal graph constructed. The goal is to obtain a refusal graph from which a canonical tester will be constructed. This transformation, denoted Tg, onlyacts on the refusal sets. The transformation of a refusal graph G =(G, L,∆,Ref , g0) is a refusal graph Tg(G) =(G, L,∆,Ref ′ , g0) where: •⌈Ref ′ (g)⌉ = {L} if ⌈Ref (g)⌉ = {L} •⌈Ref ′ (g)⌉ = Min({L \ E | E ⊆ L, E �∈ ⌈Ref (g)⌉}) if⌈Ref (g)⌉ �= {L}
170 Valéry Tschaen Concerning the refusal graph of Fig. 6.10: •⌈Ref (g0)⌉ = ⌊Ref (g0)⌋ = {{a}, {c}} •⌈Ref (g1)⌉ = ⌈Ref (g2)⌉ = ⌈Ref (g3)⌉ = {{a, b, c}} And thus: •⌈Ref ′ (g0)⌉ = {{b}, {a, c}} •⌈Ref ′ (g1)⌉ = ⌈Ref ′ (g2)⌉ = ⌈Ref ′ (g3)⌉ = {{a, b, c}} Then, Tg(G) is given in Fig. 6.11. g1 {{}} a g0 {{b}, {a, c}} b g2 {{}} c q3 {{}} Fig. 6.11. Tg(G) Roughly speaking, the value of ⌊Ref ′ (g0)⌋ means that a canonical tester has to enable whether the event b or the events a and c to a conformant implementation to avoid blocking. From RG to LTS Once the refusal graph has been transformed, it remains to construct its corresponding LTS. Definition 6.4.5 (LTS associated to a RG) From a refusal graph g0, the LTS lts(g0) may be derived according to the following recursive definition : lts(g) = � [] τ; [] a; lts(g after a) E∈⌊Ref (g)⌋ a∈init(g) \ E ⎛ [] ⎝ [] b∈ � E∈⌊Ref (g)⌋ E ⎞ b; lts(g after b) ⎠ For any LTS specification S, it has been shown that T (S) =lts(Tg(rg(S))) is a canonical tester for S [DAV93]. Consider again the specification shown in Fig. 6.7, the canonical tester obtained from the LTS specification given in Fig. 6.7 is shown in Fig. 6.12. This canonical tester has less states and transitions than the canonical testers obtained with the two previous methods. �
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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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8 Test Derivation from Timed Automa
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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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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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