The power of backtracking and the confinement of length
Timothy H. McNicholl
TL;DR
This paper explores the limitations of computable curves and arcs, demonstrating the existence of points on certain computable curves that do not belong to any computable arc, and vice versa.
Contribution
It establishes new results about the separation between points on computable curves and arcs, highlighting fundamental differences in their computability properties.
Findings
Existence of a point on a computable arc not on any computable rectifiable curve.
Existence of a point on a computable rectifiable curve with computable length not on any computable arc.
Abstract
We show that there is a point on a computable arc that does not belong to any computable rectifiable curve. We also show that there is a point on a computable rectifiable curve with computable length that does not belong to any computable arc.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Cellular Automata and Applications · Digital Image Processing Techniques