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
Circuit definitions of nondeterministic complexity classes
SIAM Journal on Computing
Complexity and real computation
Complexity and real computation
Nondeterministic NC1 computation
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
The Complexity of Polynomials and Their Coefficient Functions
CCC '07 Proceedings of the Twenty-Second Annual IEEE Conference on Computational Complexity
VPSPACE and a transfer theorem over the reals
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A measure of space for computing over the reals
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Characterizing valiant's algebraic complexity classes
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
VPSPACE and a transfer theorem over the complex field
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Counting classes and the fine structure between NC1and L
MFCS'10 Proceedings of the 35th international conference 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
Succinct algebraic branching programs characterizing non-uniform complexity classes
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Counting classes and the fine structure between NC1 and L
Theoretical Computer Science
Balancing bounded treewidth circuits
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Balancing Bounded Treewidth Circuits
Theory of Computing Systems
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In the uniform circuit model of computation, the width of a boolean circuit exactly characterises the "space" complexity of the computed function. Looking for a similar relationship in Valiant's algebraic model of computation, we propose width of an arithmetic circuit as a possible measure of space. We introduce the class VL as an algebraic variant of deterministic log-space L. In the uniform setting, we show that our definition coincides with that of VPSPACE at polynomial width. Further, todefinealgebraicvariants ofnon-deterministic space-bounded classes, we introduce the notion of "read-once" certificates for arithmetic circuits. We show that polynomial-size algebraic branching programs can be expressed as a read-once exponential sum over polynomials in VL, i.e. VBP ∈ ΣR ċ VL. We also show that ΣR ċ VBP = VBP, i.e. VBPs are stable under read-once exponential sums. Further, we show that read-once exponential sumsover a restricted class of constant-width arithmetic circuits are within VQP, and this is the largest known such subclass of poly-log-width circuits with this property.