Complexity theory of real functions
Complexity theory of real functions
The power of the middle bit of a #P function
Journal of Computer and System Sciences
Computational Complexity of Two-Dimensional Regions
SIAM Journal on Computing
Computable analysis: an introduction
Computable analysis: an introduction
The computational complexity of some julia sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Hyperbolic Julia Sets are Poly-Time Computable
Electronic Notes in Theoretical Computer Science (ENTCS)
On the Complexity of Finding Paths in a Two-Dimensional Domain II: Piecewise Straight-Line Paths
Electronic Notes in Theoretical Computer Science (ENTCS)
A Fast Algorithm for Julia Sets of Hyperbolic Rational Functions
Electronic Notes in Theoretical Computer Science (ENTCS)
Jordan Curves with Polynomial Inverse Moduli of Continuity
Electronic Notes in Theoretical Computer Science (ENTCS)
Jordan curves with polynomial inverse moduli of continuity
Theoretical Computer Science
On some complexity issues of NC analytic functions
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
| Hi-index | 0.00 |
The problems of computing single-valued, analytic branches of the logarithm and square root functions on a bounded, simply connected domain S are studied. If the boundary $\partial S$ of S is a polynomial-time computable Jordan curve, the complexity of these problems can be characterized by counting classes # P, MP (or MidBitP), and ⊕ P: The logarithm problem is polynomial-time solvable if and only if FP=# P. For the square root problem, it has been shown to have the upper bound PMP and lower bound P⊕P. That is, if P=MP then the square root problem is polynomial-time solvable, and if $P\not= \oplus P$ then the square root problem is not polynomial-time solvable.