Bounded-depth, polynomial-size circuits for symmetric functions
Theoretical Computer Science
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Bounded-width polynomial-size branching programs recognize exactly those languages in NC1
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
The expressive power of voting polynomials
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Circuit definitions of nondeterministic complexity classes
SIAM Journal on Computing
A very hard log-space counting class
Theoretical Computer Science - Special issue on structure in complexity theory
Making computation count: arithmetic circuits in the nineties
ACM SIGACT News
Non-commutative arithmetic circuits: depth reduction and size lower bounds
Theoretical Computer Science
A combinatorial algorithm for the determinant
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
On Counting AC0 Circuits with Negative Constants
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
Searching Constant Width Mazes Captures the AC0 Hierarchy
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Nondeterministic NC1 Computation
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
On TC/sup 0/, AC/sup 0/, and Arithmetic Circuits
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Matrix decomposition problem is complete for the average case
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Arithmetic Circuits and Polynomial Replacement Systems
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
CIAC '00 Proceedings of the 4th Italian Conference on Algorithms and Complexity
Arithmetic Circuits, Syntactic Multilinearity, and the Limitations of Skew Formulae
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
On the power of algebraic branching programs of width two
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
On the complexity of matrix rank and rigidity
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Counting paths in planar width 2 branching programs
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
Resource Trade-offs in Syntactically Multilinear Arithmetic Circuits
Computational Complexity
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Constant-depth arithmetic circuits have been defined and studied in [AAD97,ABL98]; these circuits yield the function classes #AC0 and GapAC0. These function classes in turn provide new characterizations of the computational power of threshold circuits, and provide a link between the circuit classes AC0 (where many lower bounds are known) and TC0 (where essentially no lower bounds are known). In this paper, we resolve several questions regarding the closure properties of #AC0 and GapAC0 and characterize #AC0 in terms of counting paths in a family of bounded-width graphs.