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
A polynomial-time computable curve whose interior has a nonrecursive measure
Theoretical Computer Science
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
On The Measure Of Two-Dimensional Regions With Polynomial-Time Computable Boundaries
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
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)
On the Complexity of Convex Hulls of Subsets of the Two-Dimensional Plane
Electronic Notes in Theoretical Computer Science (ENTCS)
Electronic Notes in Theoretical Computer Science (ENTCS)
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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 @?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 P^M^P and lower bound P^@?^P. That is, if P=MP then the square root problem is polynomial-time solvable, and if P@?P then the square root problem is not polynomial-time solvable.