Muller automaton automata theory , a Muller automaton is a type of an ω-automaton . acceptance condition separates a Muller automaton from other ω-automata.condition , i.e. the set of all states visited infinitely often must be an element of the acceptance set . 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.Formal definition Formally, a deterministic Muller-automaton is a tuple A = that consists of the following information: Q is a finite set . The elements of Q are called the states of A . Σ is a finite set called the alphabet of A . δ: Q × Σ → Q is a function, called the transition function A . q 0 is an element of Q , called the initial state. F is a set of sets of states. Formally, F ⊆ P where P is powerset of Q . F defines the acceptance condition . A accepts exactly those runs in which the set of infinitely often occurring states is an element of F non-deterministic Muller automaton , the transition function δ is replaced with a transition relation Δ that returns a set of states and initial state is q 0 is replaced by a set of initial states Q 0 . Generally, Muller automaton refers to non-deterministic Muller automaton.expressive as parity automata , Rabin Automata , Streett automata , and non-deterministic Büchi automata , to mention some, and strictly more expressive than the deterministic Büchi automata. The equivalence of the above automata and non-deterministic Muller automata can be shown very easily as the accepting conditions of these automata can be emulated using the acceptance condition of Muller automata. McNaughton's Theorem demonstrates the equivalence of non-deterministic Büchi automaton and deterministic Muller automaton. Thus, deterministic and non-deterministic Muller automaton are equivalent in terms of the languages they can accept.Transformation to non-deterministic Muller automaton Following is a list of automata constructions which transforms a type of ω-automata to a non-deterministic Muller automaton.Streett automaton Transformation to deterministic muller automaton ;Union of two deterministic muller automatonTheorem provides a procedure to transform non-deterministic Büchi automaton to deterministic Muller automaton.
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