Skip to main content
SpringerLink
Log in

Branching programs as a tool for proving lower bounds on vlsi computations and optimal algorithms for systolic arrays

  • Communications
  • Conference paper
  • First Online:
Mathematical Foundations of Computer Science 1988 (MFCS 1988)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 324))

  • 136 Accesses

Abstract

The branching programs that were studied as a nonuniform computing model providing lower bounds on the space of deterministic sequential computations are considered. It is shown that branching programs can provide lower bounds on the general model of VLSI computations — multilective circuits, and that one-time-only branching programs provide lower bounds on the area of the basic model of VLSI computations. Using this technique we obtain new lower bounds on area complexity of VLSI computations.

Another technique is introduced to prove time and area optimality of some algebraic algorithms for one-dimensional systolic arrays. A new efficient algorithm on two-way systolic array is developed for GCD problem.

This work was supported by the ŠPZV I-1/5/8 grant and the ŠPZV III-8-1/10 grant.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. BABAI, L-HAJNAL, P.-SZEMERÉDI, E.,-TURÁN, G.: A lower bound for read-once only Brancinching programs. JCSS 35 (1987), 153–162.

    Google Scholar 

  2. BOLLOBÁS, B.: Extremal Graph Theory. Academic Press, New York 1987.

    Google Scholar 

  3. BORODIN,A.-DOLEV,D.-FICH,F.E.-Paul,W.: Bounds for width two branching programs. Proc. 15th ACM STOC, ACM 1983, 87–93.

    Google Scholar 

  4. BRENT, R.P.-KUNG, H.T.: Systolic VLSI arrays for linear-time GCD computation. In: VLSI '83 (F. Anceau and E.J. Aas Eds.), North-Holland, Amsterdam 1983, 145–154.

    Google Scholar 

  5. CHANDRA,A.K.-FURST,M.L.-LIPTON,R.J.: Multiparty protocols. In: Proc. 15th ACM STOC, ACM 1983, 94–99.

    Google Scholar 

  6. FTÁČNIK, M.-HROMKOVIČ, J.: Nonlinear lower bound for real-time branching programs. Computers AI 4 (1985), No.3, 353–359.

    Google Scholar 

  7. GEDDES,K.O.: Algebraic algorithms for symbolic computation — Chapt.2, Research report, University of Waterloo, Computer Science Department 1981.

    Google Scholar 

  8. HROMKOVIČ, J.: Lower bound technique for VLSI algorithms. In Proc. IMYCS'86, Hungarian Academy of Sciences, Budapest 1986, 9–19.

    Google Scholar 

  9. HROMKOVIČ,J.: Some complexity aspects of VLSI computations. Part 1. A framework for the study of information transfer in VLSI circuits. Computers AI 7, No.3, to appear.

    Google Scholar 

  10. HROMKOVIČ,J.: Some complexity aspects of VLSI computations. Part 2. Topology of circuits and information transfer. Computers AI 7, No.4, to appear.

    Google Scholar 

  11. JUKNA,S.P.: Lower bounds on the complexity of local circuits. In: 12th MFCS'86, Lecture Notes in Computer Science 233, Springer-Verlag 1986, 440–448.

    Google Scholar 

  12. KATRIŇÁK,T.-GAVALEC,M.-GEDEONOVÁ,E.-SMÍTAL,J.: Algebra a teoretická aritmetika. ALFA — SNTL 1985 (in Slovak).

    Google Scholar 

  13. KUNG,H.T.: Use of VLSI in algebraic computation: Some suggestions. In: Proc. SYMSAC'81, ACM 1981, 218–222.

    Google Scholar 

  14. KUNG,H.T.: Let's design algorithms for VLSI systems. CMU Computer Science Dept., Technical report, 1979.

    Google Scholar 

  15. LIPSON,J.D.: Elements of Algebra and Algebraic Computing. Addison-Wesley 1981.

    Google Scholar 

  16. MASEK,W.: A fast algorithm for the String editing problem and decision graph complexity. M.Sc. Thesis, MIT, May 1976.

    Google Scholar 

  17. NEČIPORUK, E.I.: On a Boolean function. Soviet Math. Dokl. 7 (1966), 999–1000.

    Google Scholar 

  18. PROCHÁZKA, J.: Zložitost' algebraických výpočtov na niektorých modeloch počítačov. Dissertation thesis, VUSEIAR Bratislava, 1986 (in Slovak).

    Google Scholar 

  19. PROCHÁZKA, J.: The polynomial GCD-algorithm implemented in a systolic architecture. Acta Math. Com. Univ. XLVIII-XLIX (1986), 325–333.

    Google Scholar 

  20. PUDLÁK,P.-ŽÁK,S.: Space complexity of computations. Unpublished manuscript, 1982.

    Google Scholar 

  21. PUDLÁK,P.: A lower bound on complexity of branching programs. In Proc. 11th MFCS'84, Lecture Notes in Computer Science 176, Springer-Verlag 1984, 480–489.

    Google Scholar 

  22. THOMPSON, C.O.: A Complexity Theory for VLSI. Doct. dissertation, CMU-CS-80-140, Computer Science Dept., Carnegie-Mellon University, Pittsburg, August 1980.

    Google Scholar 

  23. ULLMAN,J.D.: Computational Aspects of VLSI. Comp. Science Press 1984.

    Google Scholar 

  24. WEGENER,I.: On the complexity of Branching programs and Decision trees for Qlique functions. Universität Frankfurt, Fachbereich Informatik, Int. Rept. 5/84, 1984.

    Google Scholar 

  25. WEGENER, I.: Time-space trade-offs for Branching programs. JCSS 32 (1986), 91–96.

    Google Scholar 

  26. WEGENER, I.: Optimal decision trees and one-time-only branching programs for symetric Boolean functions. Information and Control 62 (1984), 129–143.

    Google Scholar 

  27. ŽÁK,S.: An exponential lower bound for one-time only branching programs. In: Proc. 11th MFCS'84, Lecture Notes in Computer Science 176, Springer-Verlag 1984, 562–566.

    Google Scholar 

  28. COLLINS, G.E.: Subresultants and reduced polynomial remainder sequences. JACM 14 (1967), 128–142.

    Google Scholar 

  29. GRUSKA, J.: Tvorba paralelných výpočtových sietí. Research report, Institute of Technical Cybernetics of the Slovak Academy of Sciences, Bratislava 1985 (in Slovak).

    Google Scholar 

  30. KNUTH, D.E.: The art of computer programming. Vol.2: Seminumerical algorithms. Second ed., Addison-Wesley, Reading, 1981.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Theoretical Cybernetics, Comenius University, 842 15, Bratislava, Czechoslovakia

    Juraj Hromkovič & Juraj Procházka

Authors
  1. Juraj Hromkovič
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Juraj Procházka
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michal P. Chytil Václav Koubek Ladislav Janiga

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hromkovič, J., Procházka, J. (1988). Branching programs as a tool for proving lower bounds on vlsi computations and optimal algorithms for systolic arrays. In: Chytil, M.P., Koubek, V., Janiga, L. (eds) Mathematical Foundations of Computer Science 1988. MFCS 1988. Lecture Notes in Computer Science, vol 324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017159

Download citation

  • DOI: https://doi.org/10.1007/BFb0017159

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50110-7

  • Online ISBN: 978-3-540-45926-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation