Elements of an automata theory over partial orders

A model of nondeterministic nite automaton over ((nite) partial orders is introduced. It captures existential monadic second-order logic in expressive power and generalizes classical word automata and tree automata. Special forms, such as deterministic automata, are discussed, and logical and algorithmic properties are analyzed, like closure under complement and decid-ability of the nonemptiness problem. These questions are studied in the context of diierent classes of partial orders, such as trees, Mazurkiewicz traces, or rectangular grids.