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The speciﬁcation “cash withdrawal 3” is modeled semantically by three p-obligations, we call these po1 , po2 and po3 . 1 accept t2 prompt ”Transaction accepted” card back money(amount) t3-t2<5 s t3 Fig. 3. A reﬁnement of Figure 2 the result of choosing the ﬁrst operand of the palt. , 1], which is a subset of the probability set of po1 . This means that po1 po1 . The result of choosing the second palt operand is modeled semantically by po2 . The positive and negative traces of po2 are the same as for po2 , except that traces where it takes more than 20 seconds to get a reply from the bank are positive in po2 and negative in po2 .
A similar argument shows that “cash withdrawal 1” is also a reﬁnement of “cash withdrawal 3”. 10 Related Work [Seg95] uses probabilistic automata to address the problem of veriﬁcation of randomized distributed algorithms. The analysis includes timed systems, so that real-time properties can be investigated in a probabilistic setting. [Jan03] introduces a stochastic extension to statecharts called StoCharts to allow the quantiﬁcation of the time between events according to a stochastic distribution, and deﬁnes a formal semantics that can be analyzed by tools.
Pettersson and W. ): FORMATS 2005, LNCS 3829, pp. 32–48, 2005. c Springer-Verlag Berlin Heidelberg 2005 Speciﬁcation and Reﬁnement of Soft Real-Time Requirements 2 33 The Automatic Teller Machine Example We use as example a scenario where a customer withdraws money from an automatic teller machine (atm). This section gives a brief and informal explanation of the example. Figure 1 shows the ﬁrst version of the speciﬁcation. It serves two purposes. Firstly, it introduces the basic UML sequence diagram notation.
11th Conference of the International Federation of Classification Societies