Efficient model-checking of dense-time systems with time-convexity analysis

• Authors: Farn Wang
• Venue: Theoretical Computer Science
• Year: 2013

To overcome the sky-rocketing verification cost of embedded software, symbolic model-checking technology of dense-time automata has been proposed as an automated solution. The construction of a timed precondition is a central component in the technology. The general formulation for a timed precondition operator needs to check the continuity of time progress and usually results in high complexity in the construction. However, when the state space characterized by the path condition is convex, we can use a more efficient convex timed precondition operator. In this work, we discuss the concept of time-convexity that allows us to relax the restrictions on the application of the convex timed precondition operator in place of the general one. We present examples in model-checking that engender a non-time-convex space of time progress. Nevertheless, we have also identified a class of timed computation tree logic (TCTL) formulas that only characterize time-convex state spaces. This class includes several important types of TCTL formulas, including some timed inevitabilities with deadlines. We then present a new formulation for the efficient evaluation of general timed inevitabilities with non-time-convex path conditions. The new formulation also leads to a new technique for the approximate evaluation of timed inevitabilities with better precision. Finally, we report our implementation and experiments.