A new parallel algorithm for the parentheses-matching problem

The parentheses-matching problem is of crucial importance in the construction of expression tree in order to evaluate, for instance, arithmetic expressions. A new parallel algorithm is introduced in this paper to solve the parentheses-matching problem optimally (in O(log/sub 2/ n) parallel time with O(n/log/sub 2/ n) processors) on an EREW-PRAM model. An algorithm for an input string of n parentheses with a maximal nested level of log n is also presented.