Timed Automata Approach to Verification of Systems with Degradation

We focus on systems that naturally incorporate a degrading quality, such as electronic devices with degrading electric charge or broadcasting networks with decreasing power or quality of a transmitted signal. For such systems, we introduce an extension of linear temporal logic with quantitative constraints (Linear Temporal Logic with Degradation Constraints, or DLTL for short) that provides a user-friendly formalism for specifying properties involving quantitative requirements on the level of degradation. The syntax of DLTL resembles syntax of Metric Interval Temporal Logic (MITL) designed for reasoning about timed systems. Thus, we investigate their relation and a possibility of translating DLTL verification problem for systems with degradation into previously solved MITL verification problem for timed automata. We show, that through the mentioned translation, the DLTL model checking problem can be solved with limited, yet arbitrary, precision. Further, we show that probability in Markov Decision Processes can be viewed as a degrading quality and DLTL as a probabilistic linear temporal logic with quantitative operators. We discuss expressiveness of DLTL as compared with expressiveness of probabilistic temporal logics.