Model Checking of Real-time Reachability Properties Using Abstractions (regular-paper Submission for Tacas'98)

Model checking for real-time systems suuers, in practice, from the state-explosion problem: the size of the state space grows exponentially with many parameters of the system, such as the number of clocks, the size of constants, or the number of components making up the system. In order to cope with state explosion, we propose to use abstractions allowing for a reduction of the state-space while preserving reachability properties. Five such abstractions are deened, four of which are exact, that is, it suuces to examine the abstract system in order to conclude for the concrete one, while the fth one is safe, that is, sometimes no conclusion can be made. In the main abstraction, called simulation, a concrete state is mapped to a symbolic abstract state (a set of concrete states). The other four abstractions are deened on top of the simulation abstraction, and can be computed on-they in a completely orthogonal manner. Therefore, it is possible to combine them in order to obtain better reductions. A prototype implementation of these abstractions in the real-time veriication tool Kronos has permitted to verify two benchmark examples with a signiicant scale-up in size. To our knowledge, the only explorative model-checking techniques rivaling these results are also approximative and use BDDs.