Weak Büchi automaton


In computer science and automata theory, a Weak Büchi automaton is a formalism which represents a set of infinite words. A Weak Büchi automaton is a modification of Büchi automaton such that for all pair of states and belonging to the same strongly connected component, is accepting if and only if is accepting.
A Büchi automaton accepts a word if there exists a run, such that at least one state occurring infinitely often in the final state set. For Weak Büchi automata, this condition is equivalent to the existence of a run which ultimately stays in the set of accepting states.
Weak Büchi automata are strictly less-expressive than Büchi automaton and than Co-Büchi automaton.

Properties

The deterministic Weak Büchi automata can be minimized in time .
The languages accepted by Weak Büchi automata are closed under union, intersection and complementation.
Non-deterministic Weak Büchi automata are more expressive than Weak Büchi automata. As an example, the language can be decided by a weak Büchi automaton but by no deterministic Büchi automaton