On the complexity of branching programs and decision trees for clique functions
Journal of the ACM (JACM)
Entropy of contact circuits and lower bounds on their complexity
Theoretical Computer Science - International Symposium on Mathematical Foundations of Computer Science, Bratisl
New lower bounds and hierarchy results for restricted branching programs
Journal of Computer and System Sciences
Neither reading few bits twice nor reading illegally helps much
Discrete Applied Mathematics
A read-once lower bound and a (1, +k)-hierarchy for branching programs
Theoretical Computer Science
Branching programs and binary decision diagrams: theory and applications
Branching programs and binary decision diagrams: theory and applications
An Exponential Lower Bound for One-Time-Only Branching Programs
Proceedings of the Mathematical Foundations of Computer Science 1984
A Hierarchy Result for Read-Once Branching Programs with Restricted Parity Nondeterminism
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Small Pseudo-Random Sets Yield Hard Functions: New Tight Explict Lower Bounds for Branching Programs
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Proceedings of the 19th Conference on Foundations of Software Technology and Theoretical Computer Science
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We present a new lower bound technique for two types of restricted Branching Programs (BPs), namely for read-once BPs (BP1s) with restricted amount of nondeterminism and for (1, + k)-BPs. For this technique, we introduce the notion of (strictly) k-wise l-mixed Boolean functions, which generalizes the concept of l-mixedness defined by Jukna in 1988 [3]. We prove that if a Boolean function f 驴 Bn is (strictly) k-wise l-mixed, then any nondeterministic BP1 with at most k - 1 nondeterministic nodes and any (1, + k)-BP representing f has a size of at least 2驴(l). While leading to new exponential lower bounds of well-studied functions (e.g. linear codes), the lower bound technique also shows that the polynomial size hierarchy for BP1s with respect to the available amount of nondeterminism is strict. More precisely, we present a class of functions gnk 驴 Bn which can be represented by polynomial size BP1s with k nondeterministic nodes, but require superpolynomial size if only k - 1 nondeterministic nodes are available (for k = o(n1/3/ log2/3 n)). This is the first hierarchy result of this kind where the BP1 does not obey any further restrictions. We also obtain a hierarchy result with respect to k for (1, + k)-BPs as long as k = o(驴n/log n). This extends the hierarchy result of Savicky and 驴谩k [9], where k was bounded above by 1/2n1/6/log1/3 n.