Related papers: Schema Redescription in Cellular Automata: Revisit…
In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…
Many real-world optimization models contain exploitable sparsity and block structure, but this structure is often obscured in algebraic form, limiting the effectiveness of modern parallel algorithms. We propose an automatic pipeline that…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
A method for studying the qualitative dynamical properties of abstract computing machines based on the approximation of their program-size complexity using a general lossless compression algorithm is presented. It is shown that the…
This paper proposes a new logic optimization paradigm based on circuit simulation, which reduces the need for Boolean computations such as SAT-solving or constructing BDDs. The paper develops a Boolean resubstitution framework to…
We first propose algorithms for checking language equivalence of finite automata over a large alphabet. We use symbolic automata, where the transition function is compactly represented using a (multi-terminal) binary decision diagrams…
Agent-based (AB) or Cellular Automata (CA) models are rule based and are a relatively simple discrete method that can be used to simulate complex interactions of many agents or cells. The relative ease of implementing the computational…
Reversible Cellular Automata (RCA) are a particular kind of shift-invariant transformations characterized by a dynamics composed only of disjoint cycles. They have many applications in the simulation of physical systems, cryptography and…
We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of…
It is well-known that biological and social interaction networks have a varying degree of redundancy, though a consensus of the precise cause of this is so far lacking. In this paper, we introduce a topological redundancy measure for…
We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…
This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…
Given a finite set of local constraints, we seek a cellular automaton (i.e., a local and uniform algorithm) that self-stabilises on the configurations that satisfy these constraints. More precisely, starting from a finite perturbation of a…
In this paper a method is proposed which uses data mining techniques based on rough sets theory to select neighborhood and determine update rule for cellular automata (CA). According to the proposed approach, neighborhood is detected by…
Stephen Wolfram proclaimed in his 2003 seminal work "A New Kind Of Science" that simple recursive programs in the form of Cellular Automata (CA) are a promising approach to replace currently used mathematical formalizations, e.g.…
Texture recognition is one of the most important tasks in computer vision and, despite the recent success of learning-based approaches, there is still need for model-based solutions. This is especially the case when the amount of data…
In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$.…
Elementary Cellular Automata (ECA) are a well-studied computational universe that is, despite its simple configurations, capable of impressive computational variety. Harvesting this computation in a useful way has historically shown itself…
Image-based sequencing of mRNA makes it possible to see where in a tissue sample a given gene is active, and thus discern large numbers of different cell types in parallel. This is crucial for gaining a better understanding of tissue…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…