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In real-time systems, correctness depends on the time at which events occur. Examples of real-time systems include timed protocols and many embedded system controllers. Timed automata are an extension of finite-state automata that include real-valued clock variables used to measure time. Given a timed automaton, an equivalent finite-state region automaton can be constructed, which guarantees decidability. Timed model checking tools like Uppal, Kronos, and Red use specialized data structures to represent the real-valued clock variables. A different approach, called integer-discretization, is to define clock variables that can assume only integer values, but, in general, this does not preserve continuous-time semantics. This paper describes an implicit representation of the region automaton to which ordinary model checking tools can be applied directly. This approach differs from integer discretization because it is able to handle real-valued clock variables using a finite representation and preserves the continuous-time semantics of timed automata. In this framework, we introduce the GoAbstraction, a technique to reduce the size of the state space. Based on a conservative approximation of the region automaton, GoAbstraction makes it possible to verify larger systems. In order to make the abstraction precise enough to prove meaningful properties, we introduce auxiliary variables, called Go variables, that limit the drifting of clock variables in the abstract system. The paper includes preliminary experimental results showing the effectiveness of our technique using both symbolic and bounded model checking tools. |
