A Predicative Harmonization of the Time and Provable Hierarchies

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.Comment: 11 page

A Decidable Characterization of the Classes between Lintime and Exptime

caporaso @ di.uniba.it Abstract A language is defined by closure under safe iteration and under a new form of safe diagonalization that, unlike other forms of diagonalization used in literature to define sub-recursive hierarchies, is constructive and decidable. By counting the nesting levels of these schemes, an ordinal is assigned to each program. This yields a hierarchy Tα (α < ω ω) that singles-out the complexity classes DTIMEF(n cnd +e) for all c, d, e ≥ 0.