The hierarchy of boolean circuits
Computers and Artificial Intelligence
On lower bounds for read-k-times branching programs
Computational Complexity
On separating the read-k-times branching program hierarchy
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
New Lower Bounds and Hierarchy Results for Restricted Branching Programs
WG '94 Proceedings of the 20th International Workshop on Graph-Theoretic Concepts in Computer Science
Lower Bounds for Deterministic and Nondeterministic Branching Programs
FCT '91 Proceedings of the 8th International Symposium on Fundamentals of Computation Theory
On the Hierarchy of Nondeterministic Branching k-Programs
FCT '97 Proceedings of the 11th International Symposium on Fundamentals of Computation Theory
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We compare the complexities of Boolean functions for nondeterministic syntactic read-k-times branching and branching read-sk-times programs. It is shown that for each natural number k, k ≥ 2, there exists a sequence of Boolean functions such that the complexity of computation of each function of this sequence by nondeterministic syntactic branching read-k-times programs is exponentially larger (with respect to the number of variables of the Boolean function) than by nondeterministic branching read-(k ln k/ln 2 + C)-times programs, where C is a constant independent of k. Besides, it is shown that for each natural numbers N and k(N), where 4 ≤ k(N) C2 √ln N/ln ln N and C2 k and N, there exists a Boolean function in N variables such that the complexity of this function for nondeterministic syntactic read-k-times branching programs is exponentially larger (with respect to N) than for nondeterministic syntactic read-(k, ln k/ln 2 + C)-times branching programs.