Related papers: Cellular Automata: Wolfram's Metaphors for Complex…
We present applications of a cellular automaton approach to pedestrian dynamics introduced in [1,2]. It is shown that the model is able to reproduce collective effects and self-organization phenomena encountered in pedestrian traffic, e.g.…
Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by…
We present five examples where quantum finite automata (QFAs) outperform their classical counterparts. This may be useful as a relatively simple technique to introduce quantum computation concepts to computer scientists. We also describe a…
Cellular automata have long been celebrated for their ability to generate complex behaviors from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements…
This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently…
In [Wolfram 1982; Wolfram 1983; Wolfram 2002], the backtracking of one-dimensional cellular automata is to find out which of the 2n possible initial configurations of width n evolve to a specific configuration. In this paper, in…
Controlling hybrid systems is mostly very challenging due to the variety of dynamics these systems can exhibit. Inspired by the concept of differential flatness of nonlinear continuous systems and their inherent invertibility property, the…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
In the book we present main concepts of probabilistic automata theory.
We discuss the role of classical control in the context of reversible quantum cellular automata. Employing the structure theorem for quantum cellular automata, we give a general construction scheme to turn an arbitrary cellular automaton…
It is shown that irreversible classical cellular automata can be performed by quantum algorithm using additional ancilla registers. The algorithm for cellular automata states analysis has been proposed. This algorithm is based on the…
In this work we introduce a deterministic scheme of synchronization of linear and nonlinear cellular automata (CA) with complex behavior, connected through a master-slave coupling. By using a definition of Boolean derivative, we use the…
We present a spectral representation of any computation performed by a Cellular Automaton (CA) of arbitrary topology and dimensionality via an appropriate coding scheme in Fourier space that can be implemented in an analog machine ideally…
This paper introduces time window temporal logic (TWTL), a rich expressivity language for describing various time bounded specifications. In particular, the syntax and semantics of TWTL enable the compact representation of serial tasks,…
Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…
We present a novel form of Liquid Automata, using this to simulate autopoiesis, whereby living machines self-organise in the physical realm. This simulation is based on an earlier Cellular Automaton described by Francisco Varela. The basis…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
Gauge-invariance is a fundamental concept in Physics -- known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…