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2 Why We Need Model-Based Testing

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Advanced Topics 277<br />

that linearizes heaps into integer sequences to reduce checking heap isomorphism<br />

to just comparing the integer sequence equality. A survey of symmetry reductions<br />

in temporal logic model checking is given in Miller et al. (2006). The general state<br />

isomorphism problem and more related work is discussed in Veanes et al. (2007b).<br />

Reactive systems. The idea of on-the-fly testing was pioneered in the context of<br />

labeled transition systems using the IOCO theory (Tretmans and Belinfante, 1999;<br />

Brinksma and Tretmans, 2001; van der Bijl et al., 2004) and has been implemented in<br />

tools such as TorX (Tretmans and Brinksma, 2003) and TGV (Jard and Jéron, 2005).<br />

IOCO theory is a formal testing theory based on LTSs with input actions and output<br />

actions, where input actions correspond to controllable actions and output actions<br />

correspond to observable action as discussed in Section 16.1. The IOCO theory<br />

is closely related to refinement of interface automata (de Alfaro and Henzinger,<br />

2001; de Alfaro, 2004) that is based on the notion of alternating refinement (Alur<br />

et al., 1998). Refinement of interface automata supports the view of testing as a<br />

game between a tester and the IUT and is used as the basis for the conformance<br />

relation implemented in the Spec Explorer tool (Veanes et al., 2005). The idea<br />

of using reinforcement learning during on-the-fly (or online) testing is discussed<br />

in Veanes et al. (2006). The relation between IOCO and refinement of interface<br />

automata is briefly discussed in Veanes et al. (2005). The declarative view of the<br />

conformance relation in Section 16.1.1 when the IUT accepts all inputs is closely<br />

related to IOCO, whereas the operational view discussed in the same section is<br />

closely related to refinement of interface automata. The use of games for testing is<br />

pioneered in Alur et al. (1995). A recent overview of using games in testing is given<br />

in Yannakakis (2004). The main emphasis of Chapter 16 is on on-the-fly testing,<br />

offline test generation for nondeterministic systems, and related work is discussed<br />

in Nachmanson et al. (2004) and Blass et al. (2005). The view of testing as a game<br />

is also related to Markov decision processeses (Puterman, 1994; Filar and Vrieze,<br />

1996). On-the-fly testing of real-time embedded systems using model checking<br />

theory has been implemented in the Uppaal-Tron tool (Larsen et al., 2005).<br />

The multiplexing technique discussed in Section 16.6.1 is based on Campbell<br />

et al. (2005b). The inadequacy of using fully sequential time as a way to understand<br />

the runs of a distributed system was first discussed in Lamport (1978). The view<br />

presented in Campbell et al. (2005b) is consistent with Lamport’s formulation of<br />

partially ordered distributed runs. Other work related to multiplexing is discussed<br />

in Campbell et al. (2005b).<br />

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