Interval Logics for Temporal

Interval Logics for Temporal Speci cation and Veri cation by Y. S. Ramakrishna This thesis investigates temporal speci cation and veri cation techniques using a linear-time temporal logic with interval constructs. It identi es an expressive elementary logic with interval modalities, called Future Interval Logic (FIL). This logic has a natural graphical representation which, combined with its ability to nest intervals, allows intuititive speci cation of many commonly encountered temporal properties of concurrent systems. We present the rst known elementary decision procedure for an interval logic, using the method of automata. The procedure uses a novel concept of syntactic reductions between formul of the logic. FIL is a purely qualitative logic, allowing the speci cation and veri cation of permissible event orderings in a concurrent system. In the second part of the thesis we extend FIL, with a real-time metric, thus allowing the expression of real-time constraints. We provide a decision method for this logic, using the Timed-Automata of Alur and Dill. We investigate the expressive power and complexity of the logics FIL and RTFIL, and some of their extensions. Finally, we turn to the issue of combining temporal logics with decidable quanti erfree non-temporal logics. A very large class of veri cation problems are covered by such a combination, parameterized by appropriate decidable logics. We give an automatatheoretic account of a method of Plaisted, to decide the satis ability of such a logic, which uses both rigid and exible variables. This framework allows us to obtain an exponentially more e cient algorithm than the best algorithm known so far. Our approach also clari es the metalogical aspects of the method, thus making it applicable in a more general setting. The main contributions of this thesis are that it provides the rst known elementary decision method for an interval logic and, more importantly, that it extends the wellunderstood methods of automata and of tableaux to interval logics. Interval logics (and their real-time extensions) have traditionally been considered as being beyond the domain of these methods. From a less prescriptive and more descriptive standpoint, our algorithms reinforce the general applicability of the automata-theoretic framework viii for obtaining e cient decision procedures for a variety of temporal logics, as well as for their combinations with decidable non-temporal logics. From a more practical viewpoint, the graphical avour of the logic and its timing-diagram look-and-feel make it an appropriate candidate for a practical formal methods tool. ix