A Refinement of the McCreight-Meyer Union Theorem

2024/06/12 by Matthew P. Fox, Chaitanya Karamchedu, Fox, Matthew +1
Mathematics · #Computational Complexity (cs.CC) #FOS: Computer and information sciences #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2406.08600

openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using properties of Blum complexity measures and certain complexity class operators, we exhibit a total computable and non-decreasing function t_poly such that for all k, Σ_kP = Σ_kTIME(t_poly), BPP = BPTIME(t_poly), RP = RTIME(t_poly), UP = UTIME(t_poly), PP = PTIME(t_poly), Mod_kP = Mod_kTIME(t_poly), PSPACE = DSPACE(t_poly), and so forth. A similar statement holds for any collection of language classes, provided that each class is definable by applying a certain complexity class operator to some Blum complexity class.

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