On computing the determinant in small parallel time using a small number of processors
Information Processing Letters
Lower bounds for non-commutative computation
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
Small Pseudo-Random Sets Yield Hard Functions: New Tight Explict Lower Bounds for Branching Programs
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Affine Projections of Symmetric Polynomials
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Balancing Syntactically Multilinear Arithmetic Circuits
Computational Complexity
Characterizing valiant's algebraic complexity classes
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
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
Separating multilinear branching programs and formulas
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Arithmetic circuits: The chasm at depth four gets wider
Theoretical Computer Science
Arithmetic circuit lower bounds via maxrank
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Resource Trade-offs in Syntactically Multilinear Arithmetic Circuits
Computational Complexity
| Hi-index | 0.00 |
It is shown that any weakly-skew circuit can be converted into a skew circuit with constant factor overhead, while preserving either syntactic or semantic multilinearity. This leads to considering syntactically multilinear algebraic branching programs (ABPs), which are defined by a natural read-once property. A 2n/4size lower bound is proven for ordered syntactically multilinear ABPs computing an explicitly constructed multilinear polynomial in 2nvariables. Without the ordering restriction a lower bound of level 茂戮驴(n3/2/logn) is observed, by considering a generalization of a hypercube covering problem by Galvin [1].