Deciding decomposability of ideal automata into intersections or unions is in NL, with a poly-time algorithm for ideal-preserving intersection decompositions.
Moreover,|Ssep|̸= 0as otherwise ≼ would be a total order onS, contradicting the non-linearity ofA
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Decomposition of Automata recognizing Ideals
Deciding decomposability of ideal automata into intersections or unions is in NL, with a poly-time algorithm for ideal-preserving intersection decompositions.