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 automata and than Co-Büchi automata.

Properties

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The deterministic Weak Büchi automata can be minimized in time  .[1]

The languages accepted by Weak Büchi automata are closed under union and intersection but not under complementation. For example,   can be recognised by a Weak Büchi automaton but its complement   cannot.

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.

References

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  1. ^ Löding, Christof (2001). "Efficient Minimization of Deterministic Weak ω-Automata". Information Processing Letters. 79 (3): 105–109. doi:10.1016/S0020-0190(00)00183-6.