Computing longest common square subsequences

A square is a non-empty string of form Y Y. The longest common square subsequence (LCSqS) problem is to compute a longest square occurring as a subsequence in two given strings A and B. We show that the problem can easily be solved in O(n⁶) time or O(|M|n⁴) time with O(n⁴) space, where n is the length of the strings and M is the set of matching points between A and B. Then, we show that the problem can also be solved in O(σ|M|³ + n) time and O(|M|² + n) space, or in O(|M|³ log² n log log n + n) time with O(|M|³ + n) space, where σ is the number of distinct characters occurring in A and B. We also study lower bounds for the LCSqS problem for two or more strings.