Salvatore Caporaso

A predicative and decidable charcterization of the polynomial classes of languages

Characterizations of PTIME, PSPACE, the polynomial hierarchy and its elements are given, which are decidable (membership can be decided by syntactic inspection to the constructions), predicative (according to points of view by Leivant and others), and are obtained by means of increasing restrictions to course-of-values recursion on trees (represented in a dialect of Lisp).

A predicative approach to the classification problem

We harmonize many time-complexity classes DTIMEF ( f ( n )) ( f ( n ) [ges ] n ) with the PR functions (at and above the elementary level) in a transfinite hierarchy of classes of functions [Tscr ] α . Class [Tscr ] α is obtained by means of unlimited operators, namely: a variant Π of the predicative or safe recursion scheme, introduced by Leivant, and by Bellantoni and Cook, if α is a successor; and constructive diagonalization if α is a limit. Substitution ( SBST ) is discarded because the time complexity classes are not closed under this scheme. [Tscr ] α is a structure for the PR functions finer than [Escr ] α , to the point that we have [Tscr ] e 0 = [Escr ] 3 (elementary functions). Although no explicit use is made of hierarchy functions, it is proved that f ( n ) ∈ [Tscr ] α implies f ( n ) [les ] n G α ( n ) , where G α belongs to the slow growing hierarchy (of functions) studied, in particular, by Girard and Wainer.

Extending the Implicit Computational Complexity Approach to the Sub-elementary Time-Space Classes

A resource-free characterization of some complexity classes is given by means of the predicative recursion and constructive diagonalization schemes, and of restrictions to substitution. Among other classes, we predicatively harmonize in the same hierarchy ptimef, the class Ɛ of the elementary functions, and classes DTIMESPACEF(np, nq).

On a relation between uniform coding and problems of the form DTIMEF(F) =? DSPACEF(F)

Abstract. If uniform coding (Gödelization) of potentially infinite sequences of numbers can be performed in PSPACEF, then PSPACE = EXPTIME

Syntactic Characterization in LISP of the Polynominal Complexity Classes and Hierarchy

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Consistency proof without transfinite induction for a formal system for turing machines

EXPSPACE = 2-EXPTIME, and, for all p, we have

A decidable characterization of the classes between lintime and exptime

p-

Undecidability vs transfinite induction for the consistency of hyperarithmetical sets.

EXPSPACE =

Kleene, Rogers and Rice Theorems Revisited in C and in Bash

p+1

Implicit computational complexity and the exponential time-space classes

-EXPTIME; if it can be performed in LINSPACEF, we also have LINSPACE = DTIME