Recently, processor arrays to enhance the banRecently, processor arrays to enhance the bandwidth of buses and to reduce the complexity of hardwares, using optical buses instead of electronic buses, have been proposed in manyliteratures. In this paper, we first propose a constant-time algorithm for parentheses matching problemon a linear array with slotted optical buses (LASOB).Then, given an algebraic expression of length n, we also propose a cost optimal parallel algorithmthat constructs computational tree form in the steps of constant time on LASOB with n processorsby using parentheses matching algorithm. A cost optimal parallel algorithm for this problem that runsin constant time has not yet been known on any parallel computation models.