Advertisement

Communication Complexity and BDD Lower Bound Techniques

  • Ingo Wegener
Chapter

Abstract

Communication complexity as devised by Yao (1979) has found a lot of applications in the theory of networks, VLSI design, distributed computing, time-space tradeoffs, and in lower bound techniques for the complexity of Boolean functions, in particular for various restricted models of branching programs or binary decision diagrams (BDDs). A survey on lower bound techniques for BDDs based on communication complexity is given and some other BDD lower bound techniques are identified as communication complexity approach based on new variants of communication games.

Keywords

Lower Bound Boolean Function Variable Ordering Communication Complexity Outgoing Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    F. Ablayev, “Randomization and nondeterminism are incomparable for ordered read-once branching programs”, (The printed title has the misprint “comparable”.) ICALP ‘87, LNCS 1256, 1997, 195–202.MathSciNetGoogle Scholar
  2. [2]
    F. Ablayev and M. Karpinski, “A lower bound for integer multiplication on randomized ordered read-once branching programs”, ECCC Rep., 1998, 98–011.Google Scholar
  3. [3]
    N. Alon and W. Maass, “Meanders and their applications in lower bound arguments”, Journal of Computer and System Sciences, 37, 1988, 118–129.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    L. Babai, N. Nisan and M. Szegedy, “Multiparty protocols, pseudorandom generators for logspace, and time-space trade-offs”, Journal of Computer and System Sciences, 45, 1992, 204–232.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    B. Bollig, M. Sauerhoff, D. Sieling, and I. Wegener, “Hierarchy theorems for kOBDDs and kIBDDs”, Theoretical Computer Science, 205, 1992, 4560.MathSciNetGoogle Scholar
  6. [6]
    B. Bollig and I. Wegener, “Complexity theoretical results on partitioned (nondeterministic) binary decision diagrams”, MFCS ‘87, LNCS 1295, 1997, 159–168.MathSciNetGoogle Scholar
  7. [7]
    A. Borodin, A. Razborov and R. Smolensky, On lower bounds for readk-times branching programs“, Computational Complexity, 3, 1993, 1–18.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    R. E. Bryant, “Graph-based algorithms for Boolean function manipulation”, IEEE Trans. on Computers, 35, 1986, 677–691.MATHCrossRefGoogle Scholar
  9. [9]
    R. E. Bryant, “Symbolic Boolean manipulation with ordered binary decision diagrams”, ACM Computing Surveys, 24, 1992, 293–318.CrossRefGoogle Scholar
  10. [10]
    E. M. Clarke and J. M. Wing, “Formal methods: State of the art and future directions”, ACM Computing Surveys, 28, 1996, 626–643.CrossRefGoogle Scholar
  11. [11]
    J. Gergov, “Time-space tradeoffs for integer multiplication on various types of input oblivious sequential machines”, Information Processing Letters, 51, 1994, 265–269.MathSciNetCrossRefGoogle Scholar
  12. [12]
    J. Gergov and C. Memel, “Efficient Boolean manipulation with OBDD’s can be extended to FBDD’s”, IEEE Trans. on Computers, 43, 1994, 1197 1209.Google Scholar
  13. [13]
    J. Gergov and C. Memel, “MOD-2-OBDDs–a data structure that generalizes EXOR-sum-of-products and ordered binary decision diagrams”, Formal Methods in System Design, 8, 1996, 273–282.CrossRefGoogle Scholar
  14. [14]
    J. Hromkovic, “Communication Complexity and Parallel Computing”, 1997, Springer.Google Scholar
  15. [15]
    J. Jain, J. Bitner, M. Abadir, J. A. Abraham and D. S. Fussell, “Indexed BDDs: Algorithmic advances in techniques to represent and verify Boolean functions”, IEEE Trans. on Computers, 46, 1997, 1230–1245.MathSciNetCrossRefGoogle Scholar
  16. [16]
    S. Jukna, “Lower bounds on communication complexity”, Math. Logic and Its Applications, 5, 1987, 22–30.MathSciNetMATHGoogle Scholar
  17. [17]
    S. Jukna, “A note on read-k-times branching programs”, RAIROTheoretical Informatics and Applications, 29, 1995, 75–83.MathSciNetMATHGoogle Scholar
  18. [18]
    M. Krause, “Exponential lower bounds on the complexity of local and real-time branching programs”, Journal of Information Processing and Cybernetics (EIK) 24, 1988, 99–110.MATHGoogle Scholar
  19. [19]
    M. Krause, “Lower bounds for depth-restricted branching programs”, Information and Computation 91, 1991, 1–14.MathSciNetMATHCrossRefGoogle Scholar
  20. [20]
    M. Krause, “Separating GL from L, NL, co-NL and AL(=P) for oblivious Turing machines of linear access time”, RAIRO Theoretical Informatics and Applications, 26, 1992, 507–522.MATHGoogle Scholar
  21. [21]
    M. Krause and S. Waack, “On oblivious branching programs of linear length”, Information and Computation 94, 1991, 232–249.MathSciNetMATHCrossRefGoogle Scholar
  22. [22]
    E. Kushilevitz and N. Nisan, “Communication Complexity”, Cambridge University Press, 1997.Google Scholar
  23. [23]
    A. Narayan, J. Jain, M. Fujita and A. Sangiovanni-Vincentelli, “Partitioned ROBDDs — a compact, canonical and efficiently manipulable representation for Boolean functions”, IC CAD ‘86, 1996, 547–554.Google Scholar
  24. [24]
    N. Nisan and A. Wigderson, “Rounds in communication complexity revisited”, SIAM Journal on Computing, 22, 1993, 211–219.MathSciNetMATHCrossRefGoogle Scholar
  25. [25]
    M. Sauerhoff, “Lower bounds for randomized read-k-times branching programs”, STACS’98, LNCS 1373, 1998, 105–115.MathSciNetGoogle Scholar
  26. [26]
    M. Sauerhoff, Complexity theoretical results for randomized branching programs, Ph. D. Thesis, 1999.Google Scholar
  27. [27]
    M. Sauerhoff, “On the size of randomized OBDDs and read-once branching programs for k-stable functions”, STACS’99, LNCS 1563, 1998, 488–499.MathSciNetGoogle Scholar
  28. [28]
    D. Sieling and I. Wegener, “Graph driven BDDs — a new data structure for Boolean functions”, Theoretical Computer Science, 141, 1995, 283–310.MathSciNetMATHCrossRefGoogle Scholar
  29. [29]
    J. Simon and M. Szegedy, “A new lower bound theorem for read-only-once branching programs and its applications”, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 13, 1993, 183–193.MathSciNetGoogle Scholar
  30. [30]
    J. S. Thathachar, “On separating the read-k-times branching program hierarchy”, STOC’98, 1998, 653–662.Google Scholar
  31. [31]
    S. Waack, “On the descriptive and algorithmic power of parity ordered binary decision diagrams”, STACS’97, LNCS 1200, 1997, 201–212.MathSciNetGoogle Scholar
  32. [32]
    I. Wegener, The Complexity of Boolean Functions,Wiley-Teubner.Google Scholar
  33. [33]
    I. Wegener, “On the complexity of branching programs and decision trees for clique functions”, Journal of the ACM, 35, 1988, 461–471.MathSciNetMATHCrossRefGoogle Scholar
  34. [34]
    I. Wegener, “Branching Programs and Binary Decision Diagrams — Theory and Applications”, To appear: SIAM-Monographs in Discrete Mathematics and Applications, 1999.Google Scholar
  35. [35]
    A. C. Yao, “Some complexity questions related to distributed computing”, 11. STOC, 1979, 209–213.Google Scholar
  36. [36]
    A. C. Yao, “Lower bounds by probabilistic arguments”, 24. FOCS, 1983, 420–428.Google Scholar
  37. [37]
    S. Žák, “An exponential lower bound for one-time-only branching programs”, MFCS’8.4, LNCS 176, 1984, 562–566.Google Scholar

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Ingo Wegener
    • 1
  1. 1.LS 2, FB InformatikUniv. DortmundDortmundGermany

Personalised recommendations