Almost-Sure Model Checking of Infinite Paths in One-Clock Timed Automata

In this paper, we define two relaxed semantics (one based on probabilities and the other one based on the topological notion of largeness) for LTL over infinite runs of timed automata which rule out unlikely sequences of events. We prove that these two semantics match in the framework of single-clock timed automata (and only in that framework), and prove that the corresponding relaxed model-checking problems are PSPACE-Complete. Moreover, we prove that the probabilistic non-Zenoness can be decided for single-clocktimed automata in NLOGSPACE.