The power of backtracking and the confinement of length

2011/06/16 by Timothy H. McNicholl, McNicholl, Timothy H.
Computer Science · Mathematics · #03D32 #03F60 #54D05 #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Digital Image Processing Techniques #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03D32 #msc:03F60 #msc:54D05

paper · pdf · doi:10.48550/arxiv.1106.3310

arxiv created 2011/06/16 · openalex publication_date 2011/06/16 · arxiv updated 2011/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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