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 $q^{\prime }$ belonging to the same strongly connected component, $q$ is accepting if and only if $q^{\prime }$ 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 automata and than Co-Büchi automata.

Properties

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 and intersection but not under complementation. For example, $(a+b{)}^{*}{b}^{\omega }$ can be recognised by a Weak Büchi automaton but its complement $(b^{*}a{)}^{\omega }$ cannot.

Non-deterministic Weak Büchi automata are more expressive than Weak Büchi automata. As an example, the language $(a+b{)}^{*}{b}^{\omega }$ can be decided by a Weak Büchi automaton but by no deterministic Büchi automaton.

References

• Template:Cite journal