19 search results - page 1 / 4 » The Complexity of Proving the Discrete Jordan Curve Theorem |
CORR
2010
Springer
13 years 11 months ago
2010
Springer
The Jordan Curve Theorem (JCT) states that a simple closed curve divides the plane into exactly two connected regions. We formalize and prove the theorem in the context of grid gr...
CORR
2008
Springer
13 years 11 months ago
2008
Springer
This paper presents a formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar subdivisions, formal specifications and proofs assi...
DGCI
2000
Springer
14 years 3 months ago
2000
Springer
The importance of digital geometry in image processing is well documented. To understand global properties of digital spaces and manifolds we need a solid understanding of local pr...
ANTS
2000
Springer
14 years 3 months ago
2000
Springer
Abstract. Essentially all subexponential time algorithms for the discrete logarithm problem over nite elds are based on the index calculus idea. In proposing cryptosystems based on...
DCG
2007
13 years 10 months ago
2007
Motivated by Gauss’s first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bou...