... domain for static analysis by abstract interpretation. It extends a former numerical abstract domain based on Difference-Bound Matrices and allows us to represent invariants of the form (±x ± y ≤ c), where x and y are program variables and c is a real constant. We focus on giving an efficient representation based on Difference-Bound Matrices—O(n²) memory cost, where n is the number of variables—and graph-based algorithms for all common abstract operators—O(n³) time cost. This includes a normal form algorithm to test equivalence of representation and a widening operator to compute least fixpoint approximations.

Abstract. The parallel composition with observers is a well-known approach to check or test properties over formal models of concurrent and real-time systems. We present a newtechnique to reduce the size of the resulting model. Our approach has been developed for a formalism based on Timed Automata. Firstly, it discovers relevant components and clocks at each location of the observer using influence information. Secondly, it outcomes an abstraction which is equivalent to the original model up to branching-time structure and can be treated by verification tools such as Kronos [12] or OpenKronos [23]. Our experiments suggest that the approach may lead to significant time and space savings during verification phase due to state space reduction and the existence of shorter counterexamples in the optimized model. 1