Archive for Mathematical Logic· 2026Q1
A refinement of the McCreight-Meyer union theorem
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- Q1SCImago
- 2026year
Short summary
A new total computable, non-decreasing function, t_poly, is shown to precisely characterize the time bounds for numerous complexity classes, including PSPACE and BPP.
AI-generated from the title and abstract; the full text is not read.
Key points
- A new function, t_poly, is defined using properties of Blum complexity measures.
- t_poly is total computable and non-decreasing.
- The function establishes precise time bounds for complexity classes like PSPACE, BPP, RP, UP, PP, and Mod_k P.
- For example, PSPACE is shown to be equivalent to DSPACE(t_poly).
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract Using properties of Blum complexity measures and certain complexity class operators, we exhibit a total computable and non-decreasing function $$t_\textsf{poly}$$ t poly such that for all k , $$\Sigma _k\textsf{P}= \Sigma _k\textsf{TIME}(t_\textsf{poly})$$ Σ k P = Σ k TIME ( t poly ) , $$\textsf{BPP}= \textsf{BPTIME}(t_\textsf{poly})$$ BPP = BPTIME ( t poly ) , $$\textsf{RP}= \textsf{RTIME}(t_\textsf{poly})$$ RP = RTIME ( t poly ) , $$\textsf{UP}= \textsf{UTIME}(t_\textsf{poly})$$ UP = UTIME ( t poly ) , $$\textsf{PP}= \textsf{PTIME}(t_\textsf{poly})$$ PP = PTIME ( t poly ) , $$\textsf{Mod}_k\textsf{P}= \textsf{Mod}_k\textsf{TIME}(t_\textsf{poly})$$ Mod k P = Mod k TIME ( t poly ) , $$\textsf{PSPACE}= \textsf{DSPACE}(t_\textsf{poly})$$ 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.
The authors' abstract, as published at the source. Archive for Mathematical Logic, 2026 · DOI ↗
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Field: Computational Theory and Mathematics
Computational Theory and MathematicsComputer Science