Hostname: page-component-77c89778f8-vpsfw Total loading time: 0 Render date: 2024-07-19T20:07:43.608Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Complexity of the Hidden Weighted Bit Function for Various BDD Models

Published online by Cambridge University Press:  15 August 2002

Beate Bollig ,
Martin Löbbing ,
Martin Sauerhoff  and
Ingo Wegener
Beate Bollig
Affiliation:
FB Informatik, LS 2, Univ. Dortmund, 44221 Dortmund, Germany.
Martin Löbbing
Affiliation:
FB Informatik, LS 2, Univ. Dortmund, 44221 Dortmund, Germany.
Martin Sauerhoff
Affiliation:
FB Informatik, LS 2, Univ. Dortmund, 44221 Dortmund, Germany.
Ingo Wegener
Affiliation:
FB Informatik, LS 2, Univ. Dortmund, 44221 Dortmund, Germany.
Get access

Abstract

Ordered binary decision diagrams (OBDDs) and several more general BDD models have turned out to be representations of Boolean functions which are useful in applications like verification, timing analysis, test pattern generation or combinatorial optimization. The hidden weighted bit function (HWB) is of particular interest, since it seems to be the simplest function with exponential OBDD size. The complexity of this function with respect to different circuit models, formulas, and various BDD models is discussed.

Keywords

Complexitybinary decision diagramOBDDhidden weighted bit function.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 2 , March 1999 , pp. 103 - 115
Copyright
© EDP Sciences, 1999

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ablayev, F., Randomization and nondeterminism are incomparable for ordered read-once branching programs, in Proc. of ICALP '97, LNCS 1256 (1997) 195-202.
Ablayev, F. and Karpinski, M., On the power of randomized branching programs, in Proc. of ICALP '96, LNCS 1099 (1996) 348-356.
M. Agrawal and T. Thierauf, The satisfiability problem for probabilistic ordered branching programs, in Proc. 13th IEEE Conf. on Computational Complexity (1998) 81-90.
Babai, L., Pudlák, P., Rödl, V. and Szemerédi, E., Lower bounds in complexity of symmetric Boolean functions. Theoret. Comput. Sci. 74 (1990) 313-323. CrossRef
Becker, B., Drechsler, R. and Werchner, R., On the relation between BDDs and FDDs. Inform. and Comput. 123 (1997) 185-197. CrossRef
B. Bollig and I. Wegener, Partitioned BDDs vs. other BDD models, in Proc. of the Int. Workshop on Logic Synthesis IWLS '97 (1997).
Bryant, R.E., Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35 (1986) 677-691. CrossRef
Bryant, R.E., On the complexity of VLSI implementations and graph representations of Boolean functions with applications to integer multiplication. IEEE Trans. Comput. 40 (1991) 205-213. CrossRef
R.E. Bryant, Symbolic manipulation with ordered binary decision diagrams. ACM Computing Surveys 24 (1992) 293-318.
Gergov, J. and Meinel, C., 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. CrossRef
J. Håstad, Almost optimal lower bounds for small depth circuits, in Proc. of 18th STOC (1986) 6-20.
Hofmeister, T., Hohberg, W. and Köhling, S., Some notes on threshold circuits, and multiplication in depth 4. Inform. Process. Lett. 39 (1991) 219-225. CrossRef
J. Hromkovic, Communication Complexity and Parallel Computing. Springer-Verlag (1997).
Jain, J., Abraham, J.A., Bitner, J. and Fussell, D.S., Probabilistic verification of Boolean functions. Formal Methods in System Design 1 (1992) 61-115. CrossRef
I. Kremer, N. Nisan and D. Ron, On randomized one-round communication complexity, in Proc. of 27th STOC (1995) 596-605.
E. Kushilevitz and N. Nisan, Communication Complexity. Cambridge University Press (1997).
M. Löbbing, O. Schröer and I. Wegener, The theory of zero-suppressed BDDs and the number of knight's tours, in Proc. of IFIP Workshop on Applications of the Reed-Muller Expansion on Circuit Design (1995) 38-45.
A. Narayan, J. Jain, M. Fujita and A. Sangiovanni-Vincentelli, Partitioned ROBDDs--a compact, canonical and efficiently manipulable representation for Boolean functions, in Proc. of ACM/IEEE Int. Conf. on Computer Aided Design ICCAD '96 (1996) 547-554.
Sauerhoff, M., Lower bounds for randomized read-k-times branching programs, in Proc. of STACS '98, LNCS 1373 (1998) 105-115.
M. Sauerhoff. Complexity Theoretical Results for Randomized Branching Programs. PhD thesis, Univ. of Dortmund (1999).
Sauerhoff, M., On the size of randomized OBDDs and read-once branching programs for k-stable functions, in Proc. of STACS '99, LNCS 1563 (1999) 488-499.
Sieling, D. and Wegener, I., Graph driven BDDs--a new data structure for Boolean functions. Theoret. Comput. Sci. 141 (1995) 283-310. CrossRef
R. Smolensky, Algebraic methods in the theory of lower bounds for Boolean circuit complexity, in Proc. of 19th STOC (1987) 77-82.
Valiant, L.G., Short monotone formulae for the majority function. J. Algorithms 5 (1984) 363-366. CrossRef
Waack, S., On the descriptive and algorithmic power of parity ordered binary decision diagrams, in Proc. of STACS '97, LNCS 1200 (1997) 201-212.
I. Wegener, The Complexity of Boolean Functions. Wiley-Teubner (1987).