In general, the size of the DFA resulting from the union of two DFAs A and B is O(|A|.|B|) in the worst case (usually the product construction is used to compute the union).
Let's consider the class of 'synchronized DFAs' as the class of DFAs having a synchronizing word : https://en.wikipedia.org/wiki/Synchronizing_word
After looking at some examples of synchronized DFAs A and B, it seems possible to always build a synchronized DFA for the UNION of A and B with a size O(|A| + |B|) in the worst case.
Does anybody have any information, proof or paper about the union of two synchronized DFAs in O(|A| + |B|) ?
Many thanks, Luz