Complexity theory of real functions
Complexity theory of real functions
PP is as hard as the polynomial-time hierarchy
SIAM Journal on Computing
Polynomial-time 1-Turing reductions from #PH to #P
Theoretical Computer Science
Computational geometry in C
Computational Complexity of Two-Dimensional Regions
SIAM Journal on Computing
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
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
The computational complexity of distance functions of two-dimensional domains
Theoretical Computer Science
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)
Electronic Notes in Theoretical Computer Science (ENTCS)
Complexity theory for operators in analysis
Proceedings of the forty-second ACM symposium on Theory of computing
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We investigate the computational complexity of computing the convex hull of a two-dimensional set. We study this problem in the polynomial-time complexity theory of real functions based on the oracle Turing machine model. We show that the convex hull of a two-dimensional Jordan domain S is not necessarily recursively recognizable even if S is polynomial-time recognizable. On the other hand, if the boundary of a Jordan domain S is polynomial-time computable, then the convex hull of S must be NP-recognizable, and it is not necessarily polynomial-time recognizable if PNP. We also show that the area of the convex hull of a Jordan domain S with a polynomial-time computable boundary can be computed in polynomial time relative to an oracle function in #P. On the other hand, whether the area itself is a #P real number depends on the open question of whether NP=UP.