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arXiv · 2309.02748

Operations on Boolean and Alternating Finite Automata

Galina Jirásková
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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.

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Galina Jirásková. 2023-09-06. Operations on Boolean and Alternating Finite Automata. https://doi.org/10.4204/eptcs.386.1

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