Calculating an Optimal Homomorphic Algorithm for Bracket Matching

It is widely recognized that a key problem of parallel computation is in the development of both e cient and correct parallel software. Although many advanced language features and compilation techniques have been proposed to alleviate the complexity of parallel programming, much e ort is still required to develop parallelism in a formal and systematic way. In this paper, we intend to clarify this point by demonstrating a formal derivation of a correct but e cient homomorphic parallel algorithm for a simple language recognition problem known as bracket matching. To the best of our knowledge, our formal derivation leads to a novel divide-and-conquer parallel algorithm for bracket matching.