Analyzing Real-Time Systems: Theory and Tools

The main topic of this dissertation is the development and use of methods for formal reasoning about the correctness of real-time systems, in particular methods and tools to handle new classes of problems. In real-time systems the correctness of the system does not only depend on the order in which actions take place, but also the timing of the actions. The formal reasoning presented here is based on (extensions of) the model of timed automata and tools supporting this model, mainly Uppaal. Real-time systems are often part of safety critical systems e.g. control systems for planes, trains, or factories, though also everyday electronics as audio/video equipment and (mobile) phones are considered real-time systems. Often these systems are concurrent systems with a number of components interacting, and reasoning about such systems is notoriously difficult. However, since most of the systems are either safety critical or errors in the systems are costly, ensuring correctness is very important, and hence formal reasoning can play a role in increasing the reliability of real-time systems. We present two classes of cost extended timed automata, where a cost is associated to an execution of the automaton. We show that calculating the minimum cost of reaching a location in the automaton, the minimum-cost reachability problem, is decidable for both classes. Since a number of optimization problems, e.g. scheduling problems in a natural way, can be modeled using cost extended timed automata, we can now solve these problems using extensions of timed model checkers. The state-space of the simpler class, uniformly priced timed automata (UPTA), which is a subclass of linearly priced timed automata (LPTA), can effectively be represented using a slightly modified version of the well known difference bounded matrix (DBM) data-structure for representing zones, used in most timed model checkers. Using an extension of the region construction, the minimum-cost reachability problem can also be solved for LPTAs. However, the standard way of using zones for representing the state-space cannot be used for LPTAs, since there is no way of capturing the cost of states. Based on the notion of facets, zones can be split into smaller zones which can be represented by extended DBMs in an effective way. Minimum-cost reachability for both UPTAs and LPTAs have been implemented in extensions of Uppaal, and successfully tested on a number of case studies. In particular, part of the Sidmar steel production plant, which is a case study of the Esprit VHS project, has been studied. Schedulability, without considering cost and optimality, has also been addressed using standard timed automata and Uppaal. In order to solve the schedulability problem in Uppaal it proved crucial to add a number