List Homomorphic Parallel Algorithms for Bracket Matching

We present a family of parallel algorithms for simple language recognition problems involving bracket matching. The algorithms are expressed in the Bird-Meertens Formalism, exploiting only list operations which are inherently massively parallel. Our intention is to illustrate the practical efficacy with which such algorithms can be derived and expressed given the support of a well understood theoretical foundation. One of the variants produced is of particular interest in that it exploits the same theoretical result twice to produce nested parallelism. 1 Introduction In [8], we investigated an informal methodology for the generation of parallel algorithms based upon exploitation of a fundamental result from the Bird-Meertens "theory of lists". Our main example was an algorithm for the maximum segment sum problem. In this report we provide further examples of the approach. For completeness, the remainder of this section and sections 2 and 3 repeat the introductory material from [8]. Re..