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Circular Interval-valued Computers and Simulation of (Red-green) Turing Machines

Nagy Benedek, Vályi Sándor

Fundamenta Informaticae

2021

Vol. 181, nr 2-3

213--238

Interval-valued computing is a kind of massively parallel computing. It operates on specific subsets of the interval [0,1) – unions of subintervals. They serve as basic data units and are called interval-values. It was established in [9], by a rather simple observation, that interval-valued computing, as a digital computing model, has computing power equivalent to Turing machines. However, this equivalence involves an unlimited number of interval-valued variables. In [14], the equivalence with Turing machines is established using a simulation that uses only a fixed number of interval-valued variables and this number depends only on the number of states of the Turing machine – in a logarithmic way. The simulation given there allows us to extend interval-valued computations into infinite length to capture the computing power of red-green Turing machines. In this extension of [14], based on the quasi-periodic techniques used in the simulations in that paper, a reformulation of the interval-valued computations is given, named circular interval-valued computers. This reformulation enforces the finiteness of the number of used interval-valued variables by building the finiteness into the syntax rules.

A Shift-free Characterization of NP within Interval-valued Computing

Nagy B., Vályi S.

Fundamenta Informaticae

2017

Vol. 155, nr 1/2

187--207

Interval-valued computing is a new computing paradigm that is based on manipulations of interval-values. Interval-values are finite unions of intervals on the unit interval [0; 1) so this kind of computing can be considered as a continuous space machine like optical computing [25]. Based on the massive parallelism of this paradigm, various intractable problems can be solved efficiently, i.e., by polynomial number of steps. In this paper, the well-known complexity classes, NP and coNP are addressed. A specific subclass of polynomial size interval-valued computations is proven to characterize NP, that is, exactly languages with non-deterministically polynomial time complexity can be decided by interval-valued computations of this subclass. This specific subclass of interval-valued computations does not use any of the shift operators, moreover the product operator is used only in the starting section of the computation. Due to the fact that interval-valued computing is a deterministic model of computing, an analogue result can be established for the class coNP.

Comparison of selected performances of biological and electronic information processing structures

Moškon M., Zimic N., Stražar M., Mraz M.

Przegląd Elektrotechniczny

2013

R. 89, nr 2a

166--169

We present the information processing perspective on biological systems. Several metrics, similar to the ones used in digital electronic circuits, are introduced. These metrics allow us to compare biological information processing structures with their electronic counterparts, to define the ones with the best dynamical properties, analyse their compatibility and most importantly, automatize their design. Regarding the metric values obtained and used on a simple example, target applications of synthetic information processing biological structures are discussed.

W artykule opisano zagadnienie przepływu informacji w systemach biologicznych. Zastosowano tu odwzorowanie na elementach i obwodach elektronicznych, co pozwoliło na analizę ich własności, w tym dynamicznych oraz zautomatyzowanie projektowania takich modeli. Zawarto także omówienie otrzymanych wyników badań.