Neither reading few bits twice nor reading illegally helps much
Discrete Applied Mathematics
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
On Branching Programs With Bounded Uncertainty (Extended Abstract)
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Lower Bounds for Deterministic and Nondeterministic Branching Programs
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
Time-Space Tradeoffs for Branching Programs
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations 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
Super-linear time-space tradeoff lower bounds for randomized computation
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
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We propose an information-theoretic approach to proving lower bounds on the size of branching programs. The argument is based on Kraft type inequalities for the average amount of uncertainty about (or entropy of) a given input during the various stages of computation. The uncertainty is measured by the average depth of so-called 'splitting trees' for sets of inputs reaching particular nodes of the program.We first demonstrate the approach for read-once branching programs. Then, we introduce a strictly larger class of so-called 'balanced' branching programs and, using the suggested approach, prove that some explicit Boolean functions cannot be computed by balanced programs of polynomial size. These lower bounds are new since some explicit functions, which are known to be hard for most previously considered restricted classes of branching programs, can be easily computed by balanced branching programs of polynomial size.