Both deterministic and non-deterministic Muller automata recognize the ω-regular languages.
They are named after David E. Muller, an American mathematician and computer scientist, who invented them in 1963.
[1] Formally, a deterministic Muller-automaton is a tuple A = (Q,Σ,δ,q0,F) that consists of the following information: In a non-deterministic Muller automaton, the transition function δ is replaced with a transition relation Δ that returns a set of states and the initial state q0 is replaced by a set of initial states Q0.
Thus, deterministic and non-deterministic Muller automata are equivalent in terms of the languages they can accept.
Following is a list of automata constructions that each transforms a type of ω-automata to a non-deterministic Muller automaton.