Time-Space Trade-Offs in Parallel and Neural Computing

To which extend can we speak about time-space tradeoffs in the sense that, for a given problem, a faster algorithm requires more space than a slower algorithm? Furthermore, to which extend can we speak about such trade-offs in the context of parallel or neural computing? This paper aims to give an insight to these problems. The parallel computation thesis, first proposed in print in [Ch.S.76], is a relation between parallel time and sequential space. The thesis holds for the parallel model P if parallel time is polynomially related to sequential space. How should we state a “neural computation thesis”? Considering the VLSI implementation of a neural network, we suggest here that a “neural computation thesis” has to relate sequential space to parallel time and fan-ins. Meanwhile, we state some open problems and assumptions concerning the representation of logical functions and circuits by neural networks. We focus on how to use time-space trade-offs and polynomial complexity theory in designing VLSIand sizeoptimal neural networks.