Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
On the complexity of branching programs and decision trees for clique functions
Journal of the ACM (JACM)
Binary Decision Tree Test Functions
IEEE Transactions on Computers
Entropy of contact circuits and lower bounds on their complexity
Theoretical Computer Science - International Symposium on Mathematical Foundations of Computer Science, Bratisl
DAC '94 Proceedings of the 31st annual Design Automation Conference
Graph driven BDDs—a new data structure for Boolean functions
Theoretical Computer Science
On the size of binary decision diagrams representing Boolean functions
Theoretical Computer Science
Efficient OBDD-based boolean manipulation in CAD beyond current limits
DAC '95 Proceedings of the 32nd annual ACM/IEEE Design Automation Conference
Formal Methods in System Design
A simple function that requires exponential size read-once branching programs
Information Processing Letters
Dynamic variable ordering for ordered 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
Linear sifting of decision diagrams
DAC '97 Proceedings of the 34th annual Design Automation Conference
Neither reading few bits twice nor reading illegally helps much
Discrete Applied Mathematics
Linear codes are hard for oblivious read-once parity branching programs
Information Processing Letters
On the computational power of linearly transformed BDDs
Information Processing Letters
On P versus NP CO-NP for decision trees and read-once branching programs
Computational Complexity
An Exponential Lower Bound for One-Time-Only Branching Programs
Proceedings of the Mathematical Foundations of Computer Science 1984
Separating Counting Communication Complexity Classes
STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
On the Descriptive and Algorithmic Power of Parity Ordered Binary Decision Diagrams
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Lower bounds on the complexity of 1-time only branching programs
FCT '85 Fundamentals of Computation Theory
Lower Bounds for Deterministic and Nondeterministic Branching Programs
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Linear Transformations and Exact Minimization of BDDs
GLS '98 Proceedings of the Great Lakes Symposium on VLSI '98
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Linearly transformed ordered binary decision diagrams (LTOBDDs) have been suggested as a generalization of OBDDs for the representation and manipulation of Boolean functions. Instead of variables as in the case of OBDDs, parities of variables may be tested at the nodes of an LTOBDD. By this extension it is possible to represent functions in polynomial size that do not have polynomial size OBDDs, e.g., the characteristic functions of linear codes. In this paper lower bound methods for LTOBDDs and some generalizations of LTOBDDs are presented and applied to explicitly defined functions. By the lower bound results it is possible to compare the set of functions with polynomial size LTOBDDs and their generalizations with the set of functions with polynomial size representations for many other restrictions of BDDs.