Optimal Parallel Recognition of Bracket Languages on Hypercubes

Bracket languages play an important role in the syntax analysis of programming languages. We investigate the parallel recognition and analysis of these languages as a first step towards a parallel working compiler. The main result consists in the design of an appropriate algorithm, which can be executed on hypercubes as well as on related bounded degree networks. In the average case we can achieve an optimal speed-up, meaning that q processors together can analyse bracket words of length N in time O(N/q), if we restrict ourselves to employing no more than # N processors. 1 Introduction The basis for most programming languages are Context-- Free languages. It is well known that CFL's can be recognized in polylogarithmic time using a polynomial number of processors [Rei], but these results are far from being optimal with respect to the speed-up. Bracket languages as an important subclass of CFL's are also studied in the literature. So far the unique parallel algorithms for the recogniti..