What is a Systolic Algorithm?

In this paper, we show that every systolic array executes a Regular Iterative Algorithm with a strongly separating hyperplane and conversely, that every such algorithm can be implemented on a systolic array. This characterization provides us with an unified framework for describing the contributions of other authors. It also exposes the relevance of many fundamental concepts that were introduced in the sixties by Hennie, Waite and Karp, Miller and Winograd, to the present day concern of systolic array

[1]  Carver A. Mead,et al.  Concurrent Algorithms as Space-Time Recursion Equations , 1983 .

[2]  H. T. Kung.  Why systolic architectures? , 1982, Computer.

[3]  Sun-Yuan Kung,et al.  On supercomputing with systolic/wavefront array processors , 1984 .

[4]  F. Hennie.  Analysis of Bilateral Iterative Networks , 1959 .

[5]  Edward J. McCluskey.  Iterative Combinational Switching Networksߞ General Design Considerations , 1958, IRE Trans. Electron. Comput..

[6]  H. T. Kung,et al.  One-Dimensional Systolic Arrays for Multidimensional Convolution and Resampling , 1984 .

[7]  Benjamin W. Wah,et al.  The Design of Optimal Systolic Arrays , 1985, IEEE Transactions on Computers.

[8]  Robert McNaughton,et al.  Regular Expressions and State Graphs for Automata , 1960, IRE Trans. Electron. Comput..

[9]  Frederick C. Hennie,et al.  Finite-state Models for Logical Machines , 1968 .

[10]  Patrice Quinton,et al.  The systematic design of systolic arrays , 1987 .

[11]  Peter R. Cappello,et al.  Unifying VLSI Array Designs with Geometric Transformations , 1983, International Conference on Parallel Processing.

[12]  Danny Cohen,et al.  Mathematical approach to iterative computation networks , 1978, 1978 IEEE 4th Symposium onomputer Arithmetic (ARITH).

[13]  Richard M. Karp,et al.  The Organization of Computations for Uniform Recurrence Equations , 1967, JACM.

[14]  Danny Cohen,et al.  A mathematical approach to modelling the flow of data and control in computational networks , 1981 .

[15]  Rami G. Melhem,et al.  A Mathematical Model for the Verification of Systolic Networks , 1984, SIAM J. Comput..

[16]  H. T. Kung,et al.  Direct VLSI Implementation of Combinatorial Algorithms , 1979 .

[17]  H. Kung,et al.  An algebra for VLSI algorithm design , 1983 .

[18]  Jose Antonio Baptista Fortes.  Algorithm transformations for parallel processing and vlsi architecture design , 1984 .

[19]  Uri C. Weiser,et al.  Towards a Formal Treatment of VLSI Arrays , 1981 .

[20]  H. T. Kung.  The Structure of Parallel Algorithms , 1980, Adv. Comput..

[21]  H. T. Kung,et al.  Systolic Arrays for (VLSI). , 1978 .