A Predicative Harmonization of the Time and Provable Hierarchies
Salvatore Caporaso
TL;DR
This paper introduces a decidable transfinite hierarchy for imperative programs, linking complexity classes and logical fragments without using limited operators or diagonalization.
Contribution
It defines a novel hierarchy assigning ordinals to programs, connecting complexity classes with logical fragments in a decidable framework.
Findings
Identifies classes TIMEF(n^c) and TIMEF(n_c)
Relates hierarchy to Grzegorczyk classes and PA fragments
Establishes a decidable hierarchy without limited operators
Abstract
A decidable transfinite hierarchy is defined by assigning ordinals to the programs of an imperative language. It singles out: the classes TIMEF(n^c) and TIMEF(n_c); the finite Grzegorczyk classes at and above the elementary level, and the \Sigma_k-IND fragments of PA. Limited operators, diagonalization, and majorization functions are not used.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rough Sets and Fuzzy Logic · Logic, Reasoning, and Knowledge