Systolic Computations

'Et moi, . . " si j'avait su comment en revenir, je One service mathematics bas rendered the human race. It bas put common sense back n'y serais point aile.' where it belongs, on the topmost shelf next to Jules Verne the dusty canister labelled 'discarded nonsense' . Eric T. Bell The series is divergent; therefore we may be able to do something with it O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and nonlineari ties abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sci ences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One ser vice topology has rendered mathematical physics . . .'; 'One service logic has rendered computer science . . .'; 'One service category theory has rendered mathematics . . .'. All arguably true. And all statements obtainable this way form part of the raison d'ctre of this series.

Ch. 1. VLSI models. - 1. Short history of the parallel processing. - 2. Physical opportunities and limits of VLSI. - 3. Algorithms for VLSI. - Ch. 2. The complexity of VLSI computations. - 1. VLSI complexity and complexity of algorithms. - 2. Grid model of VLSI design. - 3. Complexity of parallel computations. - Ch. 3. Systolic algorithms and systolic processors. - 1. Systolic processing. - 2. Mapping systolic algorithms on systolic processors. - 3. Graphs of systolic processors. - 4. Iterations of systolic processors. - Ch. 4. The systolic programming 225. - 1. Systolic processors and supercomputers. - 2. Parallel programming languages 245. - 3. Systolic programming in UNIX environment. - Appendix 1. Library of systolic algorithms. - Appendix 2. The grammar of the SPL. - References.