A Backward and a Forward Simulation for Weighted Tree Automata ⋆

Abstract. Two types of simulations for weighted tree automata (wta) are considered. Wta process trees as input and assign a weight to them. The weights are taken from a semiring. The two considered types of simulations work for wta over additively idempotent, commutative semirings and can be used to reduce the size of wta while preserving their semantics. Such reductions are an important tool in automata toolkits.