From generic partition refinement to weighted tree automata minimization

Abstract Partition refinement is a method for minimizing automata and transition systems of various types. Recently, we have developed partition algorithm that generic in the type given system matches run time best known algorithms many concrete types systems, e.g. deterministic as well ordinary, weighted, probabilistic (labelled) systems. Genericity achieved by modelling functors on sets, coalgebras. In present work, refine analysis our to cover additional instances, notably weighted and, more generally, tree automata. For weights cancellative monoid match, non-cancellative monoids such (the additive of) tropical semiring even substantially improve, asymptotic algorithms. We implemented tool easily instantiated implementing simple interface. Moreover, are modular, refiners new obtained composing pre-implemented basic functors. Experiments show complex types, able handle with millions transitions.