Real-time interval logic for reasoning about executions of real-time programs

Research on the testing and debugging of distributed real-time programs now focuses on more formal approaches to specification and testing. Temporal logic is a natural candidate for this since it can specify properties of event and state sequences. However, the absence of any concept of real-time limits the application of temporal logic to non real-time behavior. This paper presents an extension of the interval logic of Schwartz et al. [SMSVP83], by increasing the expressive power of the logic (with respect to real time) while retaining its intuitive appeal and understandability. The extensions are added in a “layer” that can be stripped away if formal verification is the goal, or retained if timing behavior must be tested. The extensions include: the ability to deal with real time (as in [JM86b, JM86a, OW87, NA88]); more powerful interval specification mechanisms; a limited form of quantification; and the direct expression of event predicates (as in [LeD86]). Since our work is intended to yield practical tools for software testers, we emphasize the ease of expressing the complex timing properties of real-time software (e.g. periodic behavior, performance constraints), and we demonstrate the use of the interval logic on some real-time examples that represent a test of the expressiveness and understandability of the notation.