Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
The complexity of Boolean functions
The complexity of Boolean functions
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
Reduction of OBDDs in linear time
Information Processing Letters
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Dynamic variable ordering for ordered binary decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Breadth-first manipulation of very large binary-decision diagrams
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Communication complexity and parallel computing
Communication complexity and parallel computing
Communication complexity
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
On the Existence of Polynomial Time Approximation Schemes for OBDD Minimization (Extended Abstract)
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
A Non-Linear Time Lower Bound for Boolean Branching Programs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
New Bounds on the OBDD-Size of Integer Multiplication via Universal Hashing
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Bounds on the OBDD-size of integer multiplication via universal hashing
Journal of Computer and System Sciences
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Ordered binary decision diagrams (OBDDs) are nowadays the most common dynamic data structure or representation type for Boolean functions. Among the many areas of application are verification, model checking, and computer aided design. For many functions it is easy to estimate the OBDD size but asymptotically optimal bounds are only known in simple situations. In this paper, methods for proving asymptotically optimal bounds are presented and applied to the solution of some basic problems concerning OBDDs. The largest size increase by a synthesis step of π-OBDDs followed by an optimal reordering is determined as well as the largest ratio of the size of deterministic finite automata and quasi-reduced OBDDs compared to the size of OBDDs. Moreover, the worst case OBDD size of functions with a given number of 1-inputs is investigated.