arXiv subjects

Gianpiero Cattaneo

Publications and source records attributed to Gianpiero Cattaneo.

5 recordsLinked to original sources

arXiv2021

Parallel Sandpiles or Spurious Bidirectional Icepiles?

In a recent paper E. Formenti and K. Perrot (FP) introduce a global rule assumed to describe the discrete time dynamics associated with a sandpile model under the parallel application of a suitable local rule acting on d dimensional lattices of cells equipped with uniform neighborhood. In this paper we submit this approach to a critical analysis, in the simplest elementary particular case of a one-dimensional lattice, which can be divided in two parts. In the first part we prove that the FP global rule does not describe the dynamics of standard sandpiles, but rather furnishes a description of the quite different situation of height difference between consecutive piles. This is a semantic uncorrect difference of interpretation. In the second part we investigate the consequences of the uncorrect FP assumption proving that their global rule describes a bidirectional spurious dynamics of icepiles (rather than sandpiles), in the sense that this latter is the consequence of application of three local rules: bidirectional vertical rule, bidirectional horizontal rule (typical of icepiles), and a granule jump from the bottom to the top (spurious rule of the dynamics).

cs.FL↗

arXiv2017

A Distance Between Populations for n-Points Crossover in Genetic Algorithms

Genetic algorithms (GAs) are an optimization technique that has been successfully used on many real-world problems. There exist different approaches to their theoretical study. In this paper we complete a recently presented approach to model one-point crossover using pretopologies (or Cech topologies) in two ways. First, we extend it to the case of n-points crossover. Then, we experimentally study how the distance distribution changes when the number of crossover points increases.

cs.NE↗

arXiv2017

A discussion about LNG Experiment: Irreversible or Reversible Generation of the OR Logic Gate?

In a recent paper M. Lopez-Suarez, I. Neri, and L. Gammaitoni (LNG) present a concrete realization of the Boolean OR irreversible gate, but contrary to the standard Landauer principle, with an arbitrary small dissipation of energy. A Popperian good falsification! In this paper we discuss a theoretical description of the LNG device which is indeed a 3in/3out self--reversible realization of the involved OR gate, satisfying in this way the Landauer principle of no dispersion of energy, contrary to the LNG conclusions. The different point of view is due to a different interpretation of the two outputs corresponding to the inputs 10 and 01, which are considered by LNG indistinguishable so producing a non reversible realization of the standard 2in/1out gate. On the contrary, always considering these two outputs indistinguishable, by a suitable normalization function of the cantilever angles, the experimental results obtained by the LNG device coincide with the OR connective obtained from the third output of the self-reversible 3in/3out CL gate by the Inputs-Ancilla->Garbage-Output procedure. Thus, by the self-reversibility this realization is without dissipation of energy according to the Landauer principle. Furthermore, using the self-reversible Toffoli gate it is possible to obtain from the LNG device the realization of the connective AND adopting another normalization function on the cantilever angles. Finally, by other suitable normalization procedures on cantilever angles it is possible to obtain also the other logic NOR and NAND connectives, and in a more sophisticated way the XOR and NXOR connectives in a self-reversible way. All this leads to introduce a universal logic machine consisting of the LNG device plus a memory containing all the necessary angle normalization functions to produce in a self-reversible way, by choosing one of these latter, the logic connectives now listed.

cs.ET↗

arXiv2003

Towards a Theory of Conservative Computing

We extend the notion of conservativeness, given by Fredkin and Toffoli in 1982, to generic gates whose input and output lines may assume a finite number d of truth values. A physical interpretation of conservativeness in terms of conservation of the energy associated to the data used during the computation is given. Moreover, we define conservative computations, and we show that they naturally induce a new NP-complete decision problem. Finally, we present a framework that can be used to explicit the movement of energy occurring during a computation, and we provide a quantum implementation of the primitives of such framework using creation and annihilation operators on the Hilbert space C^d, where d is the number of energy levels considered in the framework.

quant-ph↗

arXiv2002

Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.

quant-ph↗