Annealing computation has recently attracted attention as it can efficiently solve combinatorial optimization problems using an Ising spin-glass model. Stochastic cellular automata annealing (SCA) is a promising algorithm that can realize fast spin-update by utilizing its parallel computing capability. However, in SCA, pinning effect control to suppress the spin-flip probability is essential, making escaping from local minima more difficult than serial spin-update algorithms, depending on the problem. This paper proposes a novel approach called APC-SCA (Autonomous Pinning effect Control SCA), where the pinning effect can be controlled autonomously by focusing on individual spin-flip. The evaluation results using max-cut, N-queen, and traveling salesman problems demonstrate that APC-SCA can obtain better solutions than the original SCA that uses pinning effect control pre-optimized by a grid search. Especially in solving traveling salesman problems, we confirm that the tour distance obtained by APC-SCA is up to 56.3% closer to the best-known compared to the conventional approach.

Reservoir computing (RC) is an attractive alternative to machine learning models owing to its computationally inexpensive training process and simplicity. In this work, we propose EnsembleBloomCA, which utilizes cellular automata (CA) and an ensemble Bloom filter to organize an RC system. In contrast to most existing RC systems, EnsembleBloomCA eliminates all floating-point calculation and integer multiplication. EnsembleBloomCA adopts CA as the reservoir in the RC system because it can be implemented using only binary operations and is thus energy efficient. The rich pattern dynamics created by CA can map the original input into a high-dimensional space and provide more features for the classifier. Utilizing an ensemble Bloom filter as the classifier, the features provided by the reservoir can be effectively memorized. Our experiment revealed that applying the ensemble mechanism to the Bloom filter resulted in a significant reduction in memory cost during the inference phase. In comparison with Bloom WiSARD, one of the state-of-the-art reference work, the EnsembleBloomCA model achieves a 43× reduction in memory cost while maintaining the same accuracy. Our hardware implementation also demonstrated that EnsembleBloomCA achieved over 23× and 8.5× reductions in area and power, respectively.

Two-state number-conserving cellular automaton (NCCA) is a cellular automaton of which cell states are 0 or 1, and the total sum of all the states of cells is kept for any time step. It is a kind of particle-based modeling of physical systems. We introduce a new structure of its value-1 patterns, which we call a “bundle pair” and a “bundle quad”. By employing this structure, we show a relation between the neighborhood size n and n - 2 NCCAs.

A digital map is a simple dynamical system that is related to various digital dynamical systems including cellular automata, dynamic binary neural networks, and digital spiking neurons. Depending on parameters and initial condition, the map can exhibit various periodic orbits and transient phenomena to them. In order to analyze the dynamics, we present two simple feature quantities. The first and second quantities characterize the plentifulness of the periodic phenomena and the deviation of the transient phenomena, respectively. Using the two feature quantities, we construct the steady-versus-transient plot that is useful in the visualization and consideration of various digital dynamical systems. As a first step, we demonstrate analysis results for an example of the digital maps based on analog bifurcating neuron models.

Some diffusive and recurrence properties of Lorentz Lattice Gas Cellular Automata (LLGCA) have been expensively studied in terms of the densities of some of the left/right static/flipping mirrors/rotators. In this paper, for any combination S of these well known scatters, we study the computational complexity of the following problem which we call PERIODICITY on the S-model: given a finite configuration that distributes only those scatters in S, whether a particle visits the starting position periodically or not. Previously, the flipping mirror model and the occupied flipping rotator model have been shown unbounded, i.e. the process is always diffusive [17]. On the other hand, PERIODICITY is shown PSPACE-complete in the unoccupied flipping rotator model [21]. In this paper, we show that PERIODICITY is PSPACE-compete in any S-model that is neither occupied, unbounded, nor static. Particularly, we prove that PERIODICITY in any unoccupied and bounded model containing flipping mirror is PSPACE-complete.

In this paper we present a novel treatment of cellular automata (CA) from an algebraic point of view. CA on monoids associated with Σ-algebras are introduced. Then an extension of Hedlund's theorem which connects CA associated with Σ-algebras and continuous functions between prodiscrete topological spaces on the set of configurations are discussed.

In this paper, we propose a modeling approach for wireless sensor networks (WSNs) that is based on non-volatile two-dimensional cellular automata (CA) and analyze the space-time dynamics of a WSN based on the proposed model. We introduce the fourth circuit element with memory function — memristor into the cells of CA to model a non-volatile CA and employ the non-volatile CA in modeling a WSN. A state transition method is designed to implement the synchronous updates of the states between the central sensor nodes and its neighbors which might behave asynchronously in sending messages to the central one. Therefore, the energy consumption in sensor nodes can be reduced by lessening the amount of exchanged information. Simulations demonstrate that the energy consumption of a WSN can be reduced greatly based on the proposed model and the lifetime of the whole network can be increased.

We introduce the notion of 'Composition', 'Union' and 'Division' of cellular automata on groups. A kind of notions of compositions was investigated by Sato [10] and Manzini [6] for linear cellular automata, we extend the notion to general cellular automata on groups and investigated their properties. We observe the all unions and compositions generated by one-dimensional 2-neighborhood cellular automata over Z2 including non-linear cellular automata. Next we prove that the composition is right-distributive over union, but is not left-distributive. Finally, we conclude by showing reformulation of our definition of cellular automata on group which admit more than three states. We also show our formulation contains the representation using formal power series for linear cellular automata in Manzini [6].

This letter studies a digital return map that is a mapping from a set of lattice points to itself. The digital map can exhibit various periodic orbits. As a typical example, we present the digital logistic map based on the logistic map. Two fundamental results are shown. When the logistic map has a unique periodic orbit, the digital map can have plural periodic orbits. When the logistic map has an unstable period-3 orbit that causes chaos, the digital map can have a stable period-3 orbit with various domain of attractions.

Due to the complicated composition of cloud and its disordered transformation, the rendering of cloud does not perfectly meet actual prospect by current methods. Based on physical characteristics of cloud, a physical cellular automata model of Dynamic cloud is designed according to intrinsic factor of cloud, which describes the rules of hydro-movement, deposition and accumulation and diffusion. Then a parallel computing architecture is designed to compute the large-scale data set required by the rendering of dynamical cloud, and a GPU-based ray-casting algorithm is implemented to render the cloud volume data. The experiment shows that cloud rendering method based on physical cellular automata model is very efficient and able to adequately exhibit the detail of cloud.

A number-conserving cellular automaton (NCCA) is a cellular automaton such that all states of cells are represented by integers and the total number of its configuration is conserved throughout its computing process. In constrast to normal cellular automata, there are infinitely many assignments of states for NCCAs with a constant state number. As for von Neumann neighbor(radius one) NCCAs with rotation-symmetry, a local function can be represented by summation of four binary functions. In this paper, we show that the minimum size of state set of rotation-symmetric von Neumann neighbor NCCA is 5 by using this representation.

We present a tight time-hierarchy theorem for nondeterministic cellular automata by using a recursive padding argument. It is shown that, if t2(n) is a time-constructible function and t2(n) grows faster than t1(n+1), then there exists a language which can be accepted by a t2(n)-time nondeterministic cellular automaton but not by any t1(n)-time nondeterministic cellular automaton.

Quantum-dot Cellular Automata (QCA) is attracting a lot of attentions due to its extremely small feature sizes and ultra low power consumption. Up to now several designs using QCA technology have been proposed. However, we found not all of the designs function properly. Further, no general design guidelines have been proposed so far. A straightforward extension of a simple functional design pattern may fail. This makes designing a large scale circuits using QCA technology an extremely time-consuming process. In this paper we show several critical vulnerabilities in the structures of primitive QCA gates and QCA interconnects, and propose a disciplinary guideline to prevent any additional plausible but malfunctioning QCA designs.

The aim of this research is the efficient cryptanalysis of the Shrinking Generator through its characterization by means of Linear Hybrid Cellular Automata. This paper describes a new known-plaintext attack based on the computation of the characteristic polynomials of sub-automata and on the generation of the Galois field associated to one of the Linear Feedback Shift Registers components of the generator. The proposed algorithm allows predicting with absolute certainty, many unseen bits of the keystream sequence, thanks to the knowledge of both registers lengths, the characteristic polynomial of one of the registers, and the interception of a variable number of keystream bits.

In this paper, we introduce and describe the computational environment that we have developed for cellular automata (CA). CA are powerful methods to understand and simulate the behavior of complex systems such as traffic jams, fluid crosscurrents, and natural disasters. In CA method, modeling of such a system or a phenomenon is to define a transition function, which determines local interactions, so-called "CA rules." However, no systematic method for design of CA rules has been established. We require a CA simulator for "trial and error" in study of modeling based on CA. Furthermore, the CA simulation environment that does not require special knowledge of a user for parallel processing is desired. The purpose of this study is to develop a comprehensive system that enables us to expedite the design of local rules and to accelerate simulations. We have implemented two kinds of simulators differing in their characteristics to improve both design efficiency and execution speed. The major difference between the two simulators is whether a source code is compiled or not. The source code is described in DORA language the authors have designed for the system. DORA language is designed for describing CA rules simply.

This paper investigates the application of the computational model of Cellular Automata (CA) for pattern classification of real valued data. A special class of CA referred to as Fuzzy CA (FCA) is employed to design the pattern classifier. It is a natural extension of conventional CA, which operates on binary string employing boolean logic as next state function of a cell. By contrast, FCA employs fuzzy logic suitable for modeling real valued functions. A matrix algebraic formulation has been proposed for analysis and synthesis of FCA. An efficient formulation of Genetic Algorithm (GA) is reported for evolution of desired FCA to be employed as a classifier of datasets having attributes expressed as real numbers. Extensive experimental results confirm the scalability of the proposed FCA based classifier to handle large volume of datasets irrespective of the number of classes, tuples, and attributes. Excellent classification accuracy has established the FCA based pattern classifier as an efficient and cost-effective solutions for the classification problem.

This paper discusses real-time language recognition by 1-dimensional one-way cellular automata (OCAs) and two-way cellular automata (CAs), focusing on limitations of the parallel computation power. To clarify the limitations, we investigate real-time recognition of cyclic strings of the form uk with u {0,1}+ and k 2. We show a version of pumping lemma for recognizing cyclic strings by OCAs, which can be used for proving that several languages are not recognizable by OCAs in real time. The paper also discusses the real-time language recognition of CAs by prefix and postfix computation, in which every prefix or postfix of an input string is also accepted, if the prefix or postfix is in the language. It is shown that there are languages L Σ+ such that L is not recognizable by OCA in real-time and the reversal of L and the concatenation LΣ* are recognizable by CA in real-time.

The capabilities of reliable computations in one-dimensional cellular automata are investigated by means of the Early Bird Problem. The problem is typical for situations in massively parallel systems where a global behavior must be achieved by only local interactions between the single elements. The cells that cause the misoperations are assumed to behave as follows. They run a self-diagnosis before the actual computation once. The result is stored locally such that the working state of a cell becomes visible to its neighbors. A non-working (defective) cell cannot modify information but is able to transmit it unchanged with unit speed. We present an O(n log (n) log (n))-time fault-tolerant solution of the Early Bird Problem.

A number-conserving cellular automaton (NCCA) is a cellular automaton (CA) such that all states of cells are represented by integers and the sum of the cell states is conserved throughout its computing process. It can be thought of as a kind of modelization of the physical conservation law of mass or energy. It is known that the local function of a two-dimensional 45-degree reflection-symmetric von Neumann neighbor NCCA can be represented by linear combinations of a binary function. In spite of the number-conserving constraints, it is possible to design an NCCA with complex rules by employing this representation. In this paper, we study the case in which the binary function depends only on the difference of two cell states, i.e., the case in which the function can be regarded as a unary one and its circuit for applying rules to a cell only need adders and a single value table look up module. Even under this constraint, it is possible to construct a logically universal NCCA.

Automata based image compression methods exploit similarities in the images to reduce the amount of memory to the essential. Our cellular automata methods are motivated due to the fact that they may be used to create images on liquid crystal displays when we add some computational functionality to the displays. For this purpose we consider image generation methods in cellular automata with some reasonable restrictions and get a representation where the color values of the images can be derived directly from the single cell states. We are interested in the capabilities of such devices and provide some benefits of this representation in image compression, even in higher dimensions.