Decomposing Permutation Automata

  title={Decomposing Permutation Automata},
  author={Isma{\"e}l Jecker and Nicolas Mazzocchi and Petra Wolf},
A deterministic finite automaton (DFA) A is composite if its language L(A) can be decomposed into an intersection ⋂k i=1 L(Ai) of languages of smaller DFAs. Otherwise, A is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and while they proved that we can decide whether a DFA is composite, the precise complexity of this problem is still open, with a doubly-exponential gap between the upper and lower bounds. In this work, we focus on permutation DFAs, i.e., those… 

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