Unary finite automata vs. arithmetic progressions

We point out a subtle error in the proof of Chrobak’s theorem that every unary NFA can be represented as a union of arithmetic progressions that is at most quadratically large. We propose a correction for this and show how Martinez’s polynomial time algorithm, which realizes Chrobak’s theorem, can be made correct accordingly. We also show that Martinez’s algorithm cannot be improved to have logarithmic space, unless L = NL.