A complexity theory based on Boolean algebra
Journal of the ACM (JACM)
Bounded-depth, polynomial-size circuits for symmetric functions
Theoretical 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
Parallel computation with threshold functions
Proc. of the conference on Structure in complexity theory
Log depth circuits for division and related problems
SIAM Journal on 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
Finite monoids and the fine structure of NC1
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations
A theorem on probabilistic constant depth Computations
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Languages which capture complexity classes
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Parity, circuits, and the polynomial-time hierarchy
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
Unbiased bits from sources of weak randomness and probabilistic communication complexity
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Complexity classes in communication complexity theory
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
On the Minimal Hardware Complexity of Pseudorandom Function Generators
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Randomized OBDDs for the most significant bit of multiplication need exponential size
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
A larger lower bound on the OBDD complexity of the most significant bit of multiplication
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
On the correlation between parity and modular polynomials
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
On the complexity of hard-core set constructions
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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We examine a powerful model of parallel computation: polynomial size threshold circuits of bounded depth (the gates compute threshold functions with polynomial weights). Lower bounds are given to separate polynomial size threshold circuits of depth 2 from polynomial size threshold circuits of depth 3, and from probabilistic polynomial size threshold circuits of depth 2. We also consider circuits of unreliable threshold gates, circuits of imprecise threshold gates and threshold quantifiers.