This project will pursue two related lines of research: (a) the semantics of parallel systems and programming constructs for parallel computation; (b) the algebraic and analytic dynamics of large quasi- neural networks for parallel computation. In (a), an investigation of programming constructs for vector computation will be carried out with multi-tasking as one of the main approaches, as in Ada for example. A theoretical foundation for parallel algorithms will be sought within the framework of partially- ordered sets of algebraic operations. Some preliminary studies have already suggested that Ada-like constructs are insufficient for efficient parallel numerical computations. This finding will be placed on a more rigorous basis by setting up a suitable algebraically- oriented theory of multi-task algorithms, with particular attention to asynchronism. In (b), studies will be continued on the dynamics of computational systems. However, the previous Turing network model will be replaced by models based on networks of threshold-logic elements analogous to McCulloch-Pitts neurons, which are called quasi-neurons. Of particular interest are the algebraic dynamics of such systems and the analytic dynamics of special models of the quasi-neurons. Related to part (a), will be a study of the mathematical foundations of asynchronism in quasi-neural networks.
