Catálogo de publicaciones - libros

Conservative logic is a mathematical model of computation that reflects some properties of microdynamical laws of physics, such as reversibility and the conservation of the internal energy of the physical system used to perform the computations. The model is based upon the Fredkin gate, a reversible and conservative three–input/three–output boolean gate which is functionally complete for boolean logic. Computations are performed by reversible circuits composed by Fredkin gates.

In this paper we introduce energy–based P systems as a parallel and distributed model of computation in which the amount of energy manipulated and/or consumed during computations is taken into account. Moreover, we show how energy–based P systems can be used to simulate reversible Fredkin circuits. The simulating systems turn out to be themselves reversible and conservative.

We propose time solutions to two much celebrated NP-complete problems, namely the 3CNF-SAT and the directed Hamiltonian Path Problem (HPP), based on AHNEPs having all resources (size, number of rules and symbols) linearly bounded by the size of the given instance. Surprisingly enough, the time for solving HPP does not depend on the number of edges of the given graph. Finally, we discuss a possible real life implementation, not of biological inspiration as one may expect according to the roots of AHNEPs, but using the facilities of the World Wide Web.

Let be a submonoid of the free monoid , and let ⊂ be a (variable length) code. is weakly -complete iff any word in is a factor of some word in [NS 03]. In this paper, we are interested by an effective computation of a weakly -complete code containing . Given a regular submonoid and given a code ⊂ , we present a method of completion which preserves the regularity of .

It has recently been shown that several computational models – trellis automata, recursive functions and Turing machines – admit characterization by resolved systems of language equations with different sets of language-theoretic operations. This paper investigates how simple the systems of equations from the computationally universal types could be while still retaining their universality. It is shown that resolved systems with two variables and two equations are as expressive as more complicated systems, while one-variable equations are “almost” as expressive. Additionally, language equations with added quotient with regular languages are shown to be able to denote every arithmetical set.

Many -complete problems can be viewed as special cases of the Common Algorithmic Problem (CAP). In a precise sense, which will be defined in the paper, one may say that CAP has a property of . In this paper we present an effective solution to the decision version of the CAP using a family of recognizer P systems with active membranes. The analysis of the solution presented here will be done from the point of view of complexity classes in P systems.

The shuffle of words ,..., is the set of words obtained by interleaving the letters of these words such that the order of appearance of all letters of each word is respected. The study of the shuffle product of words leads to the construction of an automaton whose structure is deeply connected to a family of trees which we call araucarias. We prove many structural properties of this family of trees and give some combinatorial results. The link with the minimal partial automaton which recognizes the words of the shuffle is established. Our method works for the shuffle of ≥ 2 words.