Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn

Identification of cellular automata based on incomplete observations with bounded time gaps

In this paper, the problem of identifying the cellular automata (CAs) is considered. We frame and solve this problem in the context of incomplete observations, i.e., prerecorded, incomplete configurations of the system at certain, and unknown time stamps. We consider 1-D, deterministic, two-state CAs only. An identification method based on a genetic algorithm with individuals of variable length is proposed. The experimental results show that the proposed method is highly effective. In addition, connections between the dynamical properties of CAs (Lyapunov exponents and behavioral classes) and the performance of the identification algorithm are established and analyzed

Computing vs. Genetics

This chapter first presents the interrelations between computing and genetics, which both are based on information and, particularly, self-reproducing artificial systems. It goes on to examine genetic code from a computational viewpoint. This raises a number of important questions about genetic code. These questions are stated in the form of an as yet unpublished working hypothesis. This hypothesis suggests that many genetic alterations are caused by the last base of certain codons. If this conclusive hypothesis were to be confirmed through experiementation if would be a significant advance for treating many genetic diseases

The World as Evolving Information

This paper discusses the benefits of describing the world as information, especially in the study of the evolution of life and cognition. Traditional studies encounter problems because it is difficult to describe life and cognition in terms of matter and energy, since their laws are valid only at the physical scale. However, if matter and energy, as well as life and cognition, are described in terms of information, evolution can be described consistently as information becoming more complex. The paper presents five tentative laws of information, valid at multiple scales, which are generalizations of Darwinian, cybernetic, thermodynamic, and complexity principles. These are further used to discuss the notions of life and cognition and their evolution

Cellular automata and urban studies: a literature survey

Este artigo apresenta uma pesquisa bibliográfica sobre a técnica matemática de autómatos celulares (CA) e a sua aplicação a estudos urbanos. Os modelos baseados em CA são actualmente alvo de intensa investigação não só em termos teóricos como também na sua aplicação operacional. Diversos modelos são já aplicados a diversas áreas urbanas e regiões metropolitanas em todo o mundo. É feita a apresentação da formulação clássica de CA bem como das suas primeiras aplicações a problemas geográficos e urbanos, sendo ainda discutidas as principais evoluções da técnica. É apresentada uma série de aplicações de modelos baseados em CA e é dedicada uma atenção particular às suas medidas de desempenho e a diversas abordagens de calibração dos modelos.Peer Reviewe

Model Checking Markov Chains with Actions and State Labels

In the past, logics of several kinds have been proposed for reasoning about discrete- or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state-properties and action-sequences. For this purpose, we introduce the logic asCSL which provides powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic asCSL (continuous stochastic logic). \ud In asCSL, path properties are characterized by regular expressions over actions and state-formulas. Thus, the truth value of path-formulas does not only depend on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states.\ud We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated by through an elaborate model of a scalable cellular communication system for which several properties are formalized by means of asCSL-formulas, and checked using the new procedure

Structural machines and slime mould computation

© 2017 Informa UK Limited, trading as Taylor & Francis Group. A Physarum machine is a programmable amorphous biological computer experimentally implemented in the vegetative state of true slime mould Physarum polycephalum. It comprises an amorphous yellowish mass with networks of protoplasmic veins, programmed by spatial configurations of attracting and repelling gradients. The goal of this paper to advance formalism of Physarum machines providing theoretical tools for exploration of possibilities of these machines and extension of their applications. To achieve this goal, we introduce structural machines and study their properties