Parallelism, Slides, Schemas, and Frames

In BT (Brain Theory), we study nets of simultaneously active neurons, and of interacting brain regions. In AI (Artificial Intelligence), we must structure programs for a serial computer. However, the development of a serial algorithm for a function does not preclude the existence of a more efficient parallel algorithm. For example, when adding two numbers, the propagation of the carry bit seems to force seriality. However, a look-ahead adder (see Hill and Peterson (1973) for a textbook treatment) can be built which uses parallelism based on ‘carry look-ahead’ to reduce addition time from the order of n (the length of the numbers) to the order of log n which, in fact, is the best possible (cf. Winograd’s (1965)). Our task here is to examine the ways in which behavior is best expressed in structure, and consider the extent to which we can expect parallelism in that structure. Clearly, the ‘precedence relations’ of the real world — you must walk to the door before you go through it, for example — impose a high-level seriality on the flow of computation. However, within these high-level constraints, we shall see much room for parallel computation.