Uniform closure properties of P-computable functions
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Feasible arithmetic computations: Valiant's hypothesis
Journal of Symbolic Computation
A new pebble game that characterizes parallel complexity classes
SIAM Journal on Computing
Properties that characterize LOGCFL
Journal of Computer and System Sciences
Circuit definitions of nondeterministic complexity classes
SIAM Journal on Computing
The complexity of iterated multiplication
Information and Computation
Non-commutative arithmetic circuits: depth reduction and size lower bounds
Theoretical Computer Science
Some Exact Complexity Results for Straight-Line Computations over Semirings
Journal of the ACM (JACM)
Complete Problems for Valiant's Class of qp-Computable Families of Polynomials
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
Derandomizing polynomial identity tests means proving circuit lower bounds
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The complexity of tensor calculus
Computational Complexity
Valiant's model and the cost of computing integers
Computational Complexity
The complexity of two problems on arithmetic circuits
Theoretical Computer Science
Lower Bounds for Syntactically Multilinear Algebraic Branching Programs
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
VPSPACE and a transfer theorem over the complex field
Theoretical Computer Science
On the expressive power of planar perfect matching and permanents of bounded treewidth matrices
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Small-space analogues of Valiant's classes
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
On the expressive power of CNF formulas of bounded tree- and clique-width
Discrete Applied Mathematics
VPSPACE and a transfer theorem over the complex field
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
| Hi-index | 0.00 |
Valiant introduced 20 years ago a theory to study the complexity of polynomial families. Using arithmetic circuits as computation model, these classes are easy to define and open to combinatorial techniques. In this paper we gather old and new results under a unifying theme, namely the restrictions imposed upon the gates, building a hierarchy from formulas to circuits. As a consequence we get simpler proofs for known results such as the equality of the classes VNP and VNPe or the completeness of the determinant for VQP, and new results such as a characterization of the class VP or answers to both a conjecture and a problem raised by Bürgisser [1]. We also show that for circuits of polynomial depth and unbounded size these models have the same expressive power and characterize a uniform version of VNP.