Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM (JACM)
Efficient parallel evaluation of straight-line code and arithmetic circuits
SIAM Journal on Computing
Counting classes are at least as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Counting classes: thresholds, parity, mods, and fewness
Theoretical Computer Science - Selected papers of the 7th Annual Symposium on theoretical aspects of computer science (STACS '90) Rouen, France, February 1990
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Completeness classes in algebra
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Derandomizing polynomial identity tests means proving circuit lower bounds
Computational Complexity
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Characterizing valiant's algebraic complexity classes
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
On the Sum of Square Roots of Polynomials and Related Problems
ACM Transactions on Computation Theory (TOCT)
Monomials, multilinearity and identity testing in simple read-restricted circuits
Theoretical Computer Science
| Hi-index | 5.23 |
By using arithmetic circuits, encoding multivariate polynomials may be drastically more efficient than writing down the list of monomials. Via the study of two examples, we show however that such an encoding can be hard to handle with a Turing machine even if the degree of the polynomial is low. Namely we show that deciding whether the coefficient of a given monomial is zero is hard for P^#^P under strong nondeterministic Turing reductions. As a result, this problem does not belong to the polynomial hierarchy unless this hierarchy collapses. For polynomials over fields of characteristic k0, this problem is Mod"kP-complete. This gives a coNP^M^o^d^"^k^P algorithm for deciding an upper bound on the degree of a polynomial given by a circuit in fields of characteristic k0.