Why is Boolean complexity theory difficult?
Poceedings of the London Mathematical Society symposium on Boolean function complexity
Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
Nondeterministic NC1 computation
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
The computational complexity of some problems of linear algebra
Journal of Computer and System Sciences
The complexity of matrix rank and feasible systems of linear equations
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
Rigidity of a simple extended lower triangular matrix
Information Processing Letters
Computers & Mathematics with Applications
Hi-index | 0.00 |
We revisit a well studied linear algebraic problem, computing the rank and determinant of matrices, in order to obtain completeness results for small complexity classes. In particular, we prove that computing the rank of a class of diagonally dominant matrices is complete for L. We show that computing the permanent and determinant of tridiagonal matrices over Z is in GapNC1 and is hard for NC1. We also initiate the study of computing the rigidity of a matrix: the number of entries that needs to be changed in order to bring the rank of a matrix below a given value. It is NP-hard over F2 and we prove that some restricted versions characterize small complexity classes. We also look at a variant of rigidity where there is a bound on the amount of change allowed. Using ideas from the linear interval equations literature, we show that this problem is NP-hard over Q and that a certain restricted version is NPcomplete. Restricting the problem further, we obtain variations which can be computed in PL and are hard for C=L.