We introduce layered automata, a subclass of alternating parity automata that generalises deterministic automata. Assuming a consistency property, these automata are history deterministic and 0-1 probabilistic. We show that every omega-regular language is recognised by a unique minimal consistent layered automaton, and that this canonical form can be computed in polynomial time from every layered or deterministic automaton. We further establish that for layered automata both consistency checking and inclusion testing can be performed in polynomial time. Much like deterministic finite automata, minimal consistent layered automata admit a characterisation based on congruences.

翻译：本文引入分层自动机，作为交替奇偶自动机的一个子类，其推广了确定性自动机。在满足一致性性质的前提下，这类自动机具有历史确定性与0-1概率性。我们证明每个ω-正则语言均可被唯一的最小一致分层自动机识别，且该规范形式可从任意分层自动机或确定性自动机在多项式时间内计算得到。进一步地，我们证实对于分层自动机，一致性检验与包含性测试均可在多项式时间内完成。与确定性有限自动机类似，最小一致分层自动机可通过同余关系进行刻画。