Abstract
We study the computational complexity of the Hausdorff distance of two curves on the two-dimensional plane, in the context of the Turing machine-based complexity theory of real functions. It is proved that the Hausdorff distance of any two polynomial-time computable curves is a left-Σ2P real number. Conversely, for any tally set A in Σ2P, there exist two polynomial-time computable curves such that set A is computable in polynomial time relative to the Hausdorff distance of these two curves. More generally, we show that, for any set A in Σ2P, there exist two polynomial-time computable curves such that set A is computable in polynomial time relative to the Hausdorff distances of subcurves of these two curves.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
