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
Computing algebraic formulas using a constant number of registers
SIAM Journal on Computing
Circuit definitions of nondeterministic complexity classes
SIAM Journal on Computing
Bounded-width polynomial-size Boolean formulas compute exactly those functions in AC0
Information Processing Letters
On lower bounds for read-k-times branching programs
Computational Complexity
Nondeterministic NC1 computation
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
On TC0, AC0, and arithmetic circuits
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Bounded Depth Arithmetic Circuits: Counting and Closure
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Multi-linear formulas for permanent and determinant are of super-polynomial size
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Multilinear- NC" " Multilinear- NC"
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Balancing Syntactically Multilinear Arithmetic Circuits
Computational Complexity
Arithmetizing classes around NC1and L
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
On Lower Bounds for Constant Width Arithmetic Circuits
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Balancing bounded treewidth circuits
CSR'10 Proceedings of the 5th 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
Balancing Bounded Treewidth Circuits
Theory of Computing Systems
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Functions in arithmetic NC1are known to have equivalent constant width polynomial degree circuits, but the converse containment is unknown. In a partial answer to this question, we show that syntactic multilinear circuits of constant width and polynomial degree can be depth-reduced, though the resulting circuits need not be syntactic multilinear. We then focus specifically on polynomial-size syntactic multilinear circuits, and study relationships between classes of functions obtained by imposing various resource (width, depth, degree) restrictions on these circuits. Along the way, we obtain a characterisation of NC1(and its arithmetic counterparts) in terms of log width restricted planar branching programs. We also study the power of skew formulae, and show that even exponential sums of these are unlikely to suffice to express the determinant function.