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.