CSL^TA: an Expressive Logic for Continuous-Time Markov Chains

The stochastic temporal logic CSL can be used to describe formally properties of continuous-time Markov chains, and has been extended with expressions over states and actions to obtain the logic asCSL. However, properties referring to the probability of a finite sequence of timed events (such as "with probability at least 0.75, the system will be in state set A at time 5, then in state set B at time 7, then in state set C at time 20") cannot be expressed in either CSL or asCSL. With the aim of increasing the expressive power of temporal logics for continuous- time Markov chains, we introduce the logic CSL^TA and its model-checking algorithm. CSL^TA extends CSL and asCSL by allowing the specification of timed properties through a deterministic one-clock timed automata.