Muller automaton

The Muller automaton called a 1963 imagined by David E. Muller concept of ω - automata in automata theory. This type - deterministic and non- deterministic - has the same expressive power as nondeterministic Büchi automata. Both recognize exactly the regular ω - languages. The idea of ​​Muller automata is to precisely define the infinitely visited states which, compared with Büchi automata allows more precise statements about the acceptance behavior.

  • Is the set of states
  • Is the transition function
  • , That is, for certain quantities

The Muller - acceptable ω - languages ​​are the boolean combinations of deterministic Büchi - recognizable languages. Each deterministic Büchi automaton can be expressed as a Muller automaton. Under the class of Boolean operators Muller - recognizable machine is complete. To construct a Muller automaton a ( nondeterministic ) Büchi automata, can be the Büchi automata guess which set is the correct size, infinitely through often does, and must of when to begin the runs.

Acceptance behavior

Accepts a word if the run of to be successful.

The Muller condition is: for

It needs to accept that is a certain amount of acceptance component infinitely often through completely.

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