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 $q$ and $q'$ belonging to the same strongly connected component, $q$ is accepting if and only if $q'$ is accepting.

A Büchi automaton accepts a word $w$ if there exists a run, such that at least one state occurring infinitely often in the final state set $F$. 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

Weak Büchi automata are equivalent to deterministic Weak Büchi automata. The determinization algorithm runs in exponential time. The deterministic Weak Büchi automata can be minimized in time $O(n\log(n))$.

The languages accepted by Weak Büchi automata are closed under union, intersection and complementation.

References

• Boigelot, Bernard (3 July 2005). "An effective decision procedure for linear arithmetic over the integers and reals". ACM Transactions on Computational Logic. 6 (3): 614–633. doi:10.1145/1071596.1071601.