Thermostat ( CAV 2010 ) AVACS H 4 Phase 2 July 28 , 2011

1 Description of the Model We consider in this test case an extension of the thermostat example described in [1]. A sketch of the model is depicted in Figure 1 There are four modes: Cool, Heat, Check and Error. The latter mode models the occurence of a failure, where the temperature sensor gets stuck at the last checked temperature.The set of variables {t, x, T } where T represents the temperature, t represents a local timer and x is used to measure the total time passed so far. Thus, in all modes it holds that x = 1 and t = 1. In each mode there is also an invariant constraint restricting the set of state space for this mode. Invariant constraints are only for the sake of convenience and comparison with [1]. The Figure 1: Sketch of the Thermostat model initial condition is assumed to be m = Heat ∧ t = 0 ∧ x = 0 ∧ 9 ≤ T ≤ 10. The unsafe constraint is m = Error ∧ x ≤ 5. We can interpret the probability of reaching the set of unsafe states as the probability of reaching the Error mode within time 5. Assume that 1