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Since Büchi automata are strictly more expressive than LTL, such a translation is not possible in the general case. For instance, the language $L = \{w_0 w_1 w_2 \ldots \in (2^{\{a\}})^\omega \mid \exists^\infty i \in \mathbb{N}. w_{2i} = \{a\} \}$ is representable by a Büchi automaton with 3 states, but is not expressible in LTL as it is a counting ...


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