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An incremental mechanical development of systolic solutions to the Algebraic Path Problem

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Summary

The Algebraic Path Problem, whose solution is Gauss-Jordan elimination, is one of the most complex problems for which systolic implementations have been proposed. We apply a development method which derives these systolic implementations from a traditional (i.e., Pascal-like) program by formal computational steps. The structure which our method imposes on the derivation process exposes clearly the relationship between the different implementations.

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References

  1. Boyer, R.S., Moore, J.S.: A computational logic. ACM Monograph Series. New York: Academic Press 1979

    Google Scholar 

  2. Frison, P., Gachet, P., Quinton, P.: Designing systolic arrays with DIASTOL. In: Kung, S.-Y., Owen, R.E., Nash, J.G. (eds.) VLSI signal processing II, pp. 93–105. IEEE Press 1986

  3. Huang, C.-H., Lengauer, C.: An incremental mechanical development of systolic solutions to the algebraic path problem. Technical Report TR-86-28, Department of Computer Sciences, The University of Texas at Austin, 1986

  4. Huang, C.-H., Lengauer, C.: The derivation of systolic implementations of programs. Acta Inf. 24, 595–632 (1987)

    Google Scholar 

  5. Karp, R.M., Miller, R.E., Winograd, S.: The organization of computations for uniform recurrence equations. JACM 14, 563–590 (1967)

    Google Scholar 

  6. Lengauer, C., Hehner, E.C.R.: A methodology for programming with concurrency: an informal presentation. Sci. Comp. Program. 2, 1–18 (1982)

    Google Scholar 

  7. Lengauer, C., Huang, C.-H.: A mechanically certified theorem about optimal concurrency of sorting networks. In: Proc. 13th Ann. ACM Symp. on Principles of Programming Languages, pp. 307–317 (1986)

  8. Lewis, P.S., Kung, S.Y.: Dependence graph based design of systolic arrays for the algebraic path problem. In: Etter, D.M. (ed.) Conference Record of 20th Asilomar Conference on Signals, Systems and Computers, pp. 13–18 (1986)

  9. Quinton, P.: The systematic design of systolic arrays. Technical Report 193, Publication Interne IRISA 1983. Also: TR 84-11, The Microelectronics Center of North Carolina 1984

  10. Quinton, P.: Mapping recurrences on parallel architectures. In: Supercomputing '88 (ICS 88) Vol. III: Supercomputing Design: Hardware and Software, pp. 1–8 (1988)

  11. Robert, Y.: Systolic algorithms for path-finding problems. In: Choffrut, C. (ed.) Automata Networks, pp. 68–81. Lect. Notes Comput. Sci. 316. Heidelberg New York Berlin: Springer 1986

    Google Scholar 

  12. Robert, Y., Trystram, D.: An orthogonal systolic array for the algebraic path problem. Computing 39, 187–199 (1987)

    Google Scholar 

  13. Rote, G.: A systolic array algorithm for the algebraic path problem (Shortest Paths; Matrix Inversion). Computing 34, 191–219 (1985)

    Google Scholar 

  14. Rote, G.: On the connection between hexagonal and unidirectional rectangular systolic arrays. In: VLSI Algorithms and Architectures, pp. 70–83. Lect. Notes Comput. Sci. 227. Heidelberg Berlin New York: Springer 1986

    Google Scholar 

  15. Sabata, B., Arman, F., Lengauer, C: A mechanically derived systolic implementation of pyramidal algorithms. In: Workshop on Hardware Specification, Verification and Synthesis: Mathematical Aspects. Lect. Notes Comput. Sci. Heidelberg Berlin New York: Springer 1989 (to appear)

    Google Scholar 

  16. Zimmermann, U.: Linear and combinatorial optimization in ordered algebraic structure. Annals of Discrete Mathematics 10. Amsterdam: North-Holland 1981

    Google Scholar 

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This research was partially supported by Grant No. 26-7603-35 of the Lockheed Missiles & Space Corporation and by Grant No. DCR-8610427 of the National Science Foundation

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Huang, CH., Lengauer, C. An incremental mechanical development of systolic solutions to the Algebraic Path Problem. Acta Informatica 27, 97–124 (1989). https://doi.org/10.1007/BF00265150

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