Topological rigidity of linear cellular automaton shifts

We prove that topologically isomorphic linear cellular automaton shifts are algebraically isomorphic. Using this, we show that two distinct such shifts cannot be isomorphic. We conclude that the automorphism group of a linear cellular automaton shift is a finitely generated abelian group.     

Stability of Cellular Automata Trajectories Revisited: Branching Walks and Lyapunov Profiles

We study non-equilibrium defect accumulation dynamics on a cellular automaton trajectory: a branching walk process in which a defect creates a successor on any neighborhood site whose update it affects. On an infinite lattice, defects accumulate at different exponential rates in different directions, giving rise to the Lyapunov profile. This profile quantifies instability of a cellular automaton evolution and is connected to the theory of large deviations. We rigorously and empirically study Lyapunov profiles generated from random initial states. We also introduce explicit and computationally feasible variational methods to compute the Lyapunov profiles for periodic configurations, thus developing an analog of Floquet theory for cellular automata.     

Glider-based computing in reaction-diffusion hexagonal cellular automata

A three-state hexagonal cellular automaton, discovered in [Wuensche A. Glider dynamics in 3-value hexagonal cellular automata: the beehive rule. Int J Unconvention Comput, in press], presents a conceptual discrete model of a reaction-diffusion system with inhibitor and activator reagents. The automaton model of reaction-diffusion exhibits mobile localized patterns (gliders) in its space–time dynamics. We show how to implement the basic computational operations with these mobile localizations, and thus demonstrate collision-based logical universality of the hexagonal reaction-diffusion cellular automaton.     

Some applications of propositional logic to cellular automata

In this paper we give a new proof of Richardson's theorem [31]: a global function G_?? of a cellular automaton ?? is injective if and only if the inverse of G_?? is a global function of a cellular automaton. Moreover, we show a way how to construct the inverse cellular automaton using the method of feasible interpolation from [20]. We also solve two problems regarding complexity of cellular automata formulated by Durand [12] (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximate reasoning and finite state machines to the detection of actions in video sequences

In this paper a novel approach for recognizing actions in video sequences is presented, where the information obtained from the segmentation and tracking algorithms is used as input data. First of all, the fuzzification of input data is done and this process allows to successfully manage the uncertainty inherent to the information obtained from low-level and medium-level vision tasks, to unify the information obtained from different vision algorithms into a homogeneous representation and to aggregate the characteristics of the analyzed scenario and the objects in motion. Another contribution is the novelty of representing actions by means of an automaton and the generation of input symbols for the finite automaton depending on the comparison process between objects and actions, i.e., the main reasoning process is based on the operation of automata with capability to manage fuzzy representations of all video data. The experiments on several real traffic video sequences demonstrate encouraging results, especially when no training algorithms to obtain predefined actions to be identified are required.     

Cardy's formula for some dependent percolation models

We prove Cardy's formula for rectangular crossing probabilities in dependent site percolation models that arise from a deterministic cellular automaton with a random initial state. The cellular automaton corresponds to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice  (with alternating updates of two sublattices) [7]; it may also be realized on the triangular lattice 𝕋 with flips when a site disagrees with six, five and sometimes four of its six neighbors. Received: 24 December 2001     

A Model of the joint motion of agents with a three-level hierarchy based on a cellular automaton

The collective interaction of agents for jointly overcoming (negotiating) obstacles is simulated. The simulation uses a cellular automaton. The automaton’s cells are filled with agents and obstacles of various complexity. The agents' task is to negotiate the obstacles while moving to a prescribed target point. Each agent is assigned to one of three levels, which specifies a hierarchy of subordination between the agents. The complexity of an obstacle is determined by the amount of time needed to overcome it. The proposed model is based on the probabilities of going from one cell to another.     

Markov Chain Analysis for One-Dimensional Asynchronous Cellular Automata

We consider the finite homogeneous Markov chain induced by a class of one-dimensional asynchronous cellular automata—automata that are allowed to change only one cell per iteration. Furthermore, we confine to totalistic automata, where transitions depend only on the number of 1s in the neighborhood of the current cell. We consider three different cases: (i) size of neighborhood equals length of the automaton; (ii) size of neighborhood two, length of automaton arbitrary; and (iii) size of neighborhood three, length of automaton arbitrary. For each case, the associated Markov chain proves to be ergodic. We derive simple-form stationary distributions, in case (i) by lumping states with respect to the number of 1s in the automaton, and in cases (ii) and (iii) by considering the number of 0–1 borders within the automaton configuration. For the three-neighborhood automaton, we analyze also the Markov chain at the boundary of the parameter domain, and the symmetry of the entropy. Finally, we show that if the local transition rule is exponential, the stationary probability is the Boltzmann distribution of the Ising model.     

A decision procedure for well-formed linear quantum cellular automata

In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in an observation as the squared magnitude of its amplitude. We give an efficient algorithm which decides if a linear quantum cellular automaton is well-formed. The complexity of the algorithm is O(n²) in the algebraic model of computation if the input automaton has continuous neighborhood. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 381–394 (1997)     

Three-dimensional cellular automaton simulation of tumour growth in inhomogeneous oxygen environment

Cellular automaton theory has previously been used to study cell growth. In this study, we present a three-dimensional cellular automaton model performing the growth simulation of normal and cancerous cells. The necessary nutrient supply is provided by an artificial arterial tree which is generated by constrained constructive optimization. Spatial oxygen diffusion is approximated again by a cellular automaton model. All results could be illustrated dynamically by three-dimensional volume visualization. Because of the chosen modelling approach, an extension of the model to simulate angiogenic processes is possible.     

Quantum automaton in a 1-D box

A simple cellular automaton is conjectured based on the Dirac wave equation and a diffusion confinement which attempts to emulate quantum behaviour of a particle in a 1-D box. Some features of quantum behavior such as the collapse of the wave function upon measurement, the wave-like nature of particles, and the role of virtual and non-local interactions become evident after completing a series of computations and analyzing the results. A pronounced correspondence between an automaton and a quantum particle in a 1-D box is explicated and shows promise for explaining some of the cloudy conceptual difficulties enmeshed in present quantum space-time pictures of reality.     

22号初等元胞自动机的极限语言复杂性

§1Introduction Thetaskofthispaperistosolvetheproblemproposedin[1],i.e.,toexplorethe complexityoflimitset,orequivalently,limitlanguageoftheelementarycellularautomaton ofrule22bythetoolsofformallanguagetheory.Cellularautomata(abbreviatedasCA),asmathematicalmodelsforcomplexnatural systemscontaininglargenumbersofsimpleidenticalcomponentswithlocalinteractions,havebeenwidelyusedinphysical,biological,chemicalandcomputationalsystems[2].Despitetheirsimpleconstruction,someCAcandisplayveryrichandcompl…     

Genetic algorithms and cellular automata in aquifer management

A groundwater management problem is presented involving pumping cost minimization with both well discharges and well locations as decision variables. A grid of candidate well locations is set up and optimal arrangements of wells are sought within this discrete space. A genetic algorithm approach is presented with the following particular features: (a) A suitable scaling is applied to the objective function in order to alleviate its regionally flat behavior. (b) No penalty functions are involved in constraint handling. Instead, the feasible region is transformed into a rectangular domain. The transformation introduced is proved to be bijective. (c) A binary representation of well configurations is presented and compared to a combinatorial one. The binary representation necessitates the introduction of specially designed genetic operators. Besides purely genetic algorithms, the concept of cellular automaton is introduced as the basis of an alternative formulation of the optimization problem. The lattice of the cellular automaton provides the discrete set of candidate well positions. The well configuration is represented by a group of agents occupying an equal number of lattice sites. The agents change positions as dictated by the structure of the automaton and, also, by an associated genetic algorithm, which directs the evolution of the whole scheme toward an optimal configuration. An improved performance of this approach is noted and discussed in comparison to the purely genetic algorithm schemes of the present work. A simulated annealing approach is also applied to the same problem for comparison purposes. Finally, a new and more efficient hybrid annealing–genetic approach is introduced and discussed.     

A new memetic algorithm based on cellular learning automata for solving the vertex coloring problem

Vertex coloring problem is a combinatorial optimization problem in graph theory in which a color is assigned to each vertex of graph such that no two adjacent vertices have the same color. In this paper a new hybrid algorithm which is obtained from combination of cellular learning automata (CLA) and memetic algorithm (MA) is proposed for solving the vertex coloring problem. CLA is an effective probabilistic learning model combining cellular automata and learning automaton (LA). Irregular CLA (ICLA) is a generalization of CLA in which the restriction of rectangular grid structure in CLA is removed. The proposed algorithm is based on the irregular open CLA (IOCLA) that is an extension of ICLA in which the evolution of CLA is influenced by both local and global environments. Similar to other IOCLA-based algorithms, in the proposed algorithm, local environment is constituted by neighboring LAs of any cell and the global environment consists of a pool of memes in which each meme corresponds to a certain local search method. Each meme is represented by a set of LAs from which the history of the corresponding local search method can be extracted. To show the superiority of the proposed algorithm over some well-known algorithms, several computer experiments have been conducted. The results show that the proposed algorithm performs better than other methods in terms of running time of algorithm and the required number of colors.     

A Note on Expanding Planar Real Cellular Automata

In this paper, we deal with one-parameter families of real cellular automata in R2. We prove that for a wide class of block functions from R2 to R, the corresponding real cellular automaton is expanding when the value of the parameter is large enough.     

LAND USE OPTIMIZATION USING SELF-ORGANIZING ALGORITHMS

ABSTRACT. In many spatial systems the interaction between various regions decreases dramatically with distance. This suggests that local trade-offs may be more important than global ones in land use planning and that a decentralized, parallel optimization of the individual regions may be an attractive supplement to more centralized optimization approaches. In this paper, we solve a forest planning problem using a series of decentralized approaches. The approaches can be characterized as self-organizing algorithms and are modeled in the framework of a cellular automaton. We compare our results with those obtained by more centralized approaches, viz. a large sample approach, simulated annealing, and a genetic algorithm. We find that the self-organizing algorithms generally converge much faster to solutions which are at least as good as those obtained by simulated annealing and the genetic algorithm.     

Algorithms for the intraoperative modeling of the dynamics of atrial excitation

The problem is studied of the modeling of atrial excitation in clinical conditions. The basic model requirements and the existing methods are considered for modeling the excitation dynamics of the contractile myocardium. The cellular automaton theory serves as the basis of a model. The calculations are carried out on a rectangular grid. For each pair of the cellular automaton elements, the time delay of the excitation transfer is computed. Such an approach allows us to adapt the model to the particular data obtained by electrophysiological tests.     

A new algorithm of the state-minimization for the nondeterministic finite automata

The problem of the state-minimization for the nondeterministic finite Rabin-Scott’s automata is considered. A new algorithm for this problem is obtained. The obtained algorithm has the exponential effectiveness, like the earlier-known algorithms for this problem. But each of previous algorithms amounts to the search of minimum generative system for local reaction of equal automaton of canonical form, and unlike them, we use in this paper two special functions, marking states of the given automaton.     

The dynamics of expansive invertible onesided cellular automata

Using textile systems, we prove the conjecture of Boyle and Maass that the dynamical system defined by an expansive invertible onesided cellular automaton is topologically conjugate to a topological Markov shift. We also study expansive leftmost-permutive onesided cellular automata and bipermutive endomorphisms of mixing topological Markov shifts.

     

Some algorithms for equivalent transformation of nondeterministic finite automata

In this paper we consider algorithms which allow one to combine several states of a nondeterministic finite automaton into one state. Along with the algorithms for combining states, we adduce one more algorithm for the equivalent transformation of a non-deterministic finite automaton, namely, an algorithm for adding cycles. Problems under consideration imply the development of robust computer programs.