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Linear temporal logic and deterministic Büchi automata are incomparable: DBA cannot express $FGa$, and LTL cannot express "at least each odd letter is 'a'". But sometimes it is interesting to know whether the language of a DBA can be expressed in LTL.

I need an algorithm that decides whether a language of a given DBA is describable in LTL. Do you know algorithms for that?

Gilles 'SO- stop being evil'
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Ayrat
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2 Answers2

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You may find the algorithm in Diekert and Gastin's paper, Section 12. It works for both NBW and DBW (provided that you have the $\omega$-expression), and this can be decided in polynomial time.

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I would like to support the comment of @Wanwei Liu since the proof, including the decision procedure, is indeed in the referenced paper.

However, I would like to clarify, that the given decision procedure is proven to be PSPACE-complete, and no proof of P-time decidability is known to me or any field-related capacities I know.

Tereza Kinská
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