Probabilistic Timed I/O Automata with Continuous State Spaces

We present Piecewise Deterministic Timed I/O Automata (PDTIOA): a new continuous state automaton model that allows both nondeterministic and probabilistic discrete transitions, along with continuous deterministic trajectories. We use a partition of actions, called tasks and a task scheduler to resolve nondeterministic choice over actions. We define a topology on the set of trajectories and make a key continuity assumption about maximal length of trajectories. Together, these structures enable us to construct a natural probability measure over the space of executions and the space of traces. The resulting PDTIOA framework yields simple notions of external behavior and implementation, and has simple compositionality properties. By introducing local schedulers, we generalize PDTIOAs to allow nondeterministic trajectories and stopping times.