2018/05/07 by Masaki Nakanishi, Nakanishi, Masaki, Marcos Villagra +1
Computer Science · #Algorithms and Data Compression #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #FOS: Computer and information sciences #cs.CC #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1805.02572
16 pages
arxiv created 2018/05/07 · openalex publication_date 2018/05/07 · arxiv updated 2018/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we study the space complexity of computable real numbers represented by fast convergent Cauchy sequences. We show the existence of families of trascendental numbers which are logspace computable, as opposed to algebraic irrational numbers which seem to required linear space. We characterized the complexity of space-bounded real numbers by quantifying the space complexities of tally sets. The latter result introduces a technique to prove the space complexity of real numbers by studying its corresponding tally sets, which is arguably a more natural approach. Results of this work present a new approach to study real numbers whose transcendence is unknown.