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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 efficient and correct parallel software. Although many advanced language features and compilation techniques have been proposed to alleviate the complexity of parallel programming, much effort 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 efficient 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.