Complexity theory of real functions
Complexity theory of real functions
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 computing the logarithm and square root functions on a complex domain
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Electronic Notes in Theoretical Computer Science (ENTCS)
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Computational complexity of two-dimensional domains whose boundaries are polynomial-time computable Jordan curves with polynomial inverse moduli of continuity is studied. It is shown that the membership problem of such a domain can be solved in P^N^P, i.e., in polynomial time relative to an oracle in NP, in contrast to the higher upper bound P^M^P for domains without the property of polynomial inverse modulus of continuity. On the other hand, the lower bound of UP for the membership problem still holds for domains with polynomial inverse moduli of continuity. It is also shown that the path problem of such a domain can be solved in PSPACE, matching its known lower bound, while no fixed upper bound was known for domains without this property.