Giovanni Pani

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.

HSFS: A Compress Filesystem for Metadata Files

In this paper we propose a solution to improve the search among compress data. A Linux filesystem have been implemented by combining the advantages of squashfs (compression) and hixosfs (for research). We test our idea with DICOM file used to store medical images.

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).

IFHNFS: fast indexing information in mobile devices

Abstract To track movements of objects and people we need to use expensive technologies and complex softwares. Usually these softwares need lots of memory. There are many examples of objects and people of which would be useful to know the precise locations. Something sent via pony express, position of buses in the city, friends’ locations, and so on. Our purpose is to use connectivity of smartphone to share position via gps by using only a filesystem created ad hoc without databases or user space programs. IFHNFS is based on Hixosfs and NFS (Linux kernel). Indexing the most relevant data directly in the fs structure makes the exchange of data Faster and, via NFS, potentially available whenever and whenever. Ad-hoc solutions for Android have been developed in real contexts. The system have been tested on a network of Android OS devices that share data with a Linux server.

A Refinement of the μ-measure for Stack Programs

Abstract We analyze the complexity of a programming language operating on stacks, introducing a syntactical measure σ such that to each program P a natural number σ( P ) is assigned; the measure considers the influence on the complexity of programs of nesting loops and, simultaneously, of sequences of non-size-increasing subprograms. We prove that functions computed by stack programs of σ measure n have a length bound b∈ E n+2 (the n+2-th Grzegorczyk class), that is |f( w → )|≤b(| w → |) . This result represents an improvement with respect to the bound obtained via the μ-measure presented in [L. Kristiansen and K.-H. Niggl, On the computational complexity of imperative programming languages. Theoretical Computer Science, to appear].