By Manfred Broy, Bengt Jonsson, Joost-Pieter Katoen, Martin Leucker, Alexander Pretschner

Testing is the first and software program verification process utilized by at the present time. frequently, it's advert hoc, mistakes services, and intensely dear. lately, despite the fact that, many makes an attempt were made to boost extra refined formal checking out tools. This coherent e-book presents an in-depth evaluate of this rising box, concentrating on formal trying out of reactive systems.

This publication relies on a seminar held in Dagstuhl citadel, Germany, in January 2004. It provides 19 conscientiously reviewed and revised lectures given on the seminar in a well-balanced manner making sure powerfuble complementary insurance of all suitable facets. An appendix offers a thesaurus for model-based checking out and fundamentals on finite kingdom machines and on labelled transition platforms. The lectures are offered in topical sections on checking out of finite kingdom machines, trying out of labelled transition platforms, model-based try out case iteration, instruments and case reports, standardized attempt notation and execution architectures, and past testing.

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An ADS for machine M6 ([LY94]). Example. Consider machine M6 shown in Fig. 8. A possible ADS for this machine is given in Fig. 9. Suppose that the initial state of M6 is s6 . Then, the execution of this ADS will be as follows. We ﬁrst apply a which is the label of the root of the ADS. The machine returns 1 and moves to s1 . Since 1 is observed, the tester follows the right branch and applies b. The machine returns 0 and 2 State Identiﬁcation 51 remains at s1 . Notice that here the ADS has only one branch, that is, we know that no matter what the initial state was, after the input sequence ab the second output will certainly be 0.

It is widely believed that such problems do not have polynomial time algorithms, not even if nondeterminism is allowed. It is interesting to note that Q -homing and Q -synchronizing sequences are not polynomially bounded: as we will see later in this section, there are machines that have synchronizing sequences but only of exponential length. The following theorem was proved by Rystsov [Rys83]. 2 in Section 3. 22 ([Rys83]). The following problems, taking as input a Mealy machine M and a subset Q ⊆ S of its states, are PSPACE-complete: (1) Does M have an Q -homing sequence?

M3 is a minimal machine. Indeed, state s1 can be distinguished from states s2 and s3 by input b, and states s2 and s3 can be distinguished by input sequence ab. However, machine M3 has no distinguishing sequence. We can see this by arguing as follows. If we start by applying input symbol a on M3 and then observe output symbol 0 we can only deduce that the initial state of the machine is either s1 or s2 . Next, whatever we apply in the future the machine will have the same behavior independently of whether its initial state has been s1 or s2 .