Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Acta Informatica
Monotone circuits for connectivity require super-logarithmic depth
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Threshold circuits of bounded depth
Journal of Computer and System Sciences
Some combinatorial-algebraic problems from complexity theory
Discrete Mathematics - Special issue: trends in discrete mathematics
Top-down lower bounds for depth-three circuits
Computational Complexity
Computational Complexity - Special issue on circuit complexity
The Shrinkage Exponent of de Morgan Formulas is 2
SIAM Journal on Computing
A lower bound for depth-3 circuits with MOD m gates
Information Processing Letters
Exponential lower bounds for depth three boolean circuits
Computational Complexity
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
An Exponential Lower Bound for Depth 3 Arithmetic Circuits
An Exponential Lower Bound for Depth 3 Arithmetic Circuits
Depth Reduction for Circuits with a Single Layer of Modular Counting Gates
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
SIAM Journal on Computing
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By the complexity of a graph we mean the minimum number of union and intersection operations needed to obtain the whole set of its edges starting from stars. This measure of graphs is related to the circuit complexity of boolean functions.We prove some lower bounds on the complexity of explicitly given graphs. This yields some new lower bounds for boolean functions, as well as new proofs of some known lower bounds in the graph-theoretic framework. We also formulate several combinatorial problems whose solution would have intriguing consequences in computational complexity.