Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
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
Journal of the ACM (JACM)
Parallel computation with threshold functions
Journal of Computer and System Sciences - Structure in Complexity Theory Conference, June 2-5, 1986
Perceptrons: expanded edition
Monotone circuits for connectivity require super-logarithmic depth
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
I/O complexity: The red-blue pebble game
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Threshold functions and bounded deptii monotone circuits
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
On monotone formulae with restricted depth
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Borel sets and circuit complexity
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Size-depth trade-offs for threshold circuits
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Finite Limits and Monotone Computations: The Lower Bounds Criterion
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Tight bounds for monotone switching networks via fourier analysis
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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This paper contains two parts. In Part I, we show that polynomial-size monotone threshold circuits of depth k form a proper hierarchy in parameter k. This implies in particular that monotone TC0 is properly contained in NC1. In Part II, we introduce a new concept, called local function, which tries to characterize when a function can be efficiently computed using only localized processing elements. It serves as a unifying framework for viewing related and sometimes apparently unrelated results. In particular, it will be demonstrated that the recent results on lower bounds for monotone circuits by Razborov [Ra1] and Karchmer and Wigderson [KW], as well as a main theorem in Part I of this paper, can be regarded as proving certain functions to be nonlocal. We will also suggest an approach based on locality for attacking the conjecture that (nonmonotone) TC0 is properly contained in NC1.