Confluence reduction for Markov automata

Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. As expected, the state space explosion threatens the analysability of these models. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep them small by omitting internal transitions. We define the notion of confluence directly on Markov automata, and discuss additionally how to syntactically detect confluence on the process-algebraic language MAPA that was introduced recently. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude.