Quantitative Model Checking of Systems with Degradation

In this paper we describe a rather specialized quality of a system -- the degradation. We demonstrate systems that naturally incorporate degradation phenomenon and we show how these systems can be verified by adapting the standard automata-based approach to LTL model checking. We introduce B\"uchi Automata with Degradation Constraints (BADCs) to specify the desired properties of systems with degradation and we describe how these can be used for verification. A major obstacle in the verification process is that the synchronous product of the system and the B\"uchi automaton may be infinite, which we deal with by introducing a normal form of the B\"uchi automata and normalizing procedure. We also show that the newly introduced formalism can be used to distinguish MDPs indistinguishable by any LTL, PCTL or even PCTL* formula.