Problems of some regularities in strings, such as repetition, period, seed, square, etc., have been studied extensively recently. Many algorithms have been proposed to solve these problems in O(1) time complexity on an n imes n reconfigurable bus model, where $n$ is the length of the given string. In this paper, we concentrate to solve problems of another form of regularity, the string superprimitivity test problem and the LCS (longest common subsequence) problem in strings on the reconfigurable bus model. And we propose a O(log n) time parallel algorithm to solve the string superprimitivity test problem. We also review some algorithms for the LCS problem. Further research is also given in this paper.