the DFA-intersection computation problem, given two DFAs specified on the input, compute the intersection DFA, or the decision problem to determine its emptiness, turns out to have wider/ deeper significance in computational complexity theory. it is O(n2) time with no better lower bounds known, and tight bounds possibly having major implications on multiple complexity class separations. looking for insight/ refs.
what is the best known space complexity of determining DFA intersection (emptiness)? how does the best known algorithm work?
 Deciding emptiness of intersection of regular languages in subquadratic time / cstheory SE
 Two DFA intersection emptiness connections to SETH & L vs P / cstheory SE