The power of expression of a computational language or model has a substantive impact on the development of algorithms, and therefore on the computational complexity of a problem. Parallel processing is required to dramatically increase present computational abilities. A discussion of parallel processor design goals is followed by a description of an elegant, powerful parallel processing language extension, the Myrias PAR DO and it's associated memory semantics. The architecture of the Myrias 4000 system, which supports the parallel memory model, is briefly described. Parallel algorithms for cycle-intensive computations are presented, along with the recursive parallel method of programming and the Eureka! jump.