Limiting factors in highly parallel computation that stem from timing, communication, and reliability requirements are studied. Particular emphasis is placed on large regular structures, which are especially well suited for signal processing and iterative scientific computation, such as solving differential equations and simulating cellular automata. Computers with a million or more processors will be needed in some of these applications and mathematical results are needed to guide designer's decisions on synchronization method, memory organization and use of redundancy. The over-riding concern is whether the cost of systems can be made to grow slowly enough with the amount of parallelism. Ideally, the goal is to ensure linear speedup - a proportionate return on hardware investment. In the area of timing, work continues in statistical modeling of clock skew in synchronous systems, the analysis of throughput in self-timed arrays, and an ongoing comparison between these two synchronization paradigms. In synchronous systems all processing in different computational elements is simultaneously triggered by a signal called clock. Clock skew arises when the clock signal must travel different distances in order to reach all parts of a system. This may cause the system to work incorrectly. In self-timed systems, different elements do not assume their computations are synchronized and exchange "hand- shaking" signals everytime they need to synchronize. This may render the system slower due to overhead. In the area of communication, work continues on bounds based on pebbling arguments. These bounds on throughput depend only on memory bandwidth, and reveal the constraining effect of that resource. A major problem in parallel processing with large number of processors is to ensure that data is available for all processors to operate on. This data must be present in the memory of the different elements and/or be input/output to the machine. The availability of data ultimately determines computational speed. Analogous questions about the reliability of large parallel arrays are addressed. The question of whether or not linear speedup is attainable with fixed reliability is a central problem here, and is the subject of theoretical work.
