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We investigate the accepting state complexity of deterministic finiteautomata for regular languages obtained by applying one of the followingoperations to languages accepted by permutation automata: union, quotient,complement, difference, intersection, Kleene star, Kleene plus, and reversal.The paper thus joins the study of accepting state complexity of regularitypreserving language operations which was initiated by the work [J. Dassow: Onthe number of accepting states of finite automata, J. Autom., Lang. Comb., 21,2016]. We show that for almost all of the operations, except for reversal andquotient, there is no difference in the accepting state complexity forpermutation automata compared to deterministic finite automata in general. Forboth reversal and quotient we prove that certain accepting state complexitiescannot be obtained; these number are called "magic" in the literature.Moreover, we solve the left open accepting state complexity problem for theintersection of unary languages accepted by permutation automata anddeterministic finite automata in general.

On the Accepting State Complexity of Operations on Permutation Automata