Operations on Boolean and Alternating Finite Automata

Abstract

We examine the complexity of basic regular operations on languages represented by Boolean and alternating finite automata. We get tight upper bounds m + n and m + n + 1 for union, intersection, and difference, 2 m + n and 2 m + n + 1 for concatenation, 2 n + n and 2 n + n + 1 for square, m and m + 1 for left quotient, 2 m and 2 m + 1 for right quotient. We also show that in both models, the complexity of complementation and symmetric difference is n and m + n, respectively, while the complexity of star and reversal is 2 n . All our witnesses are described over a unary or binary alphabets, and whenever we use a binary alphabet, it is always optimal.