Abstract
Ordered binary decision diagrams (OBDDs) are nowadays one of the most common dynamic data structures or representation types for Boolean functions. Among the many areas of application are verification, model checking, computer aided design, relational algebra, and symbolic graph algorithms. Although many exponential lower bounds on the OBDD size of Boolean functions are known, there are only few functions where the OBDD size is asymptotically known exactly. In this paper the exact OBDD sizes of the fundamental functions multiplexer and addition of n-bit numbers are determined.
Similar content being viewed by others
References
Bollig, B.: The optimal read-once branching program complexity for the direct storage access function. Inf. Process. Lett. 106, 171–174 (2008)
Bollig, B., Wegener, I.: Asymptotically optimal bounds for OBDDs and the solution of some basic OBDD problems. J. Comput. Syst. Sci. 61, 558–579 (2000)
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35, 677–691 (1986)
Hromkovič, J.: Communication Complexity and Parallel Computing. Springer, Berlin (1997)
Kushilevitz, E., Nisan, N.: Communication Complexity. Cambridge University Press, Cambridge (1997)
Sieling, D., Wegener, I.: NC-algorithms for operations on binary decision diagrams. Parallel Process. Lett. 48, 139–144 (1993)
Wegener, I.: The Complexity of Boolean Functions. Wiley, New York (1987)
Wegener, I.: Branching Programs and Binary Decision Diagrams—Theory and Applications. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bollig, B., Range, N. & Wegener, I. Exact OBDD Bounds for Some Fundamental Functions. Theory Comput Syst 47, 593–609 (2010). https://doi.org/10.1007/s00224-009-9217-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-009-9217-3