Languages of Dot-Depth 3/2

Abstract We show that level 3/2 of the dot-depth hierarchy is decidable. More precisely, we identify a pattern  $\mathbb{B}$ such that the following holds: If F is a deterministic finite automaton that accepts L, then L belongs to level 3/2 of the dot-depth hierarchy if and only if F does not have $\mathbb{B}$ as a subgraph in its transition graph. The latter condition can be tested in nondeterministic logarithmic space.

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