Partitioned Cellular Automata Research Articles

Time-reversal symmetries in two-dimensional reversible partitioned cellular automata and their applications

Time-reversal symmetry (T-symmetry) in a reversible cellular automaton (CA) is the property in which forward and backward evolutions of configurations are governed by the same local transition function. We show that the framework of partitioned cellular automata (PCAs) is useful to study T-symmetries of reversible CAs. Here, we investigate reversible elementary square PCAs (ESPCAs) and reversible elementary triangular PCAs (ETPCAs), and prove that a large number of reversible ESPCAs and all reversible ETPCAs are T-symmetric under some kinds of simple transformations on configurations. As applications, these results are used to find and analyse backward evolution processes in reversible PCAs. For example, for a given functional module implemented in a reversible PCA, such as a reversible logic element, we can obtain its inverse functional module very easily using its T-symmetry.

Corrosion behavior of marine structural steel in tidal zone based on wire beam electrode technology and partitioned cellular automata model

The initial corrosion evolution of marine structural steel in tidal zone is studied using wire beam electrode (WBE). The electrochemical experiment results show that the WBE in the high and middle tidal zones are in the anodic dissolution state for less time than that in the low tidal and immersion zones. The fitting results of WBE experiment provide the boundary conditions for the partitioned cellular automata (PCA) model, which is adopted to simulate the initial corrosion evolutions of steel in the tidal zone. The proposed independent variable of the electrolyte concentration (ρ), corrosion probability (Pc), passivation probability (Pp), and movement direction probability (Pm) on the corrosion behavior of steel are studied. The calculated results demonstrate that ρ and Pm can well characterize the corrosion evolutions of the steel in ocean tidal zones. This model is effective in predicting the corrosion evolution of marine structural steel in tidal zone. It provides a new method for predicting the corrosion evolution of marine structural steel in tidal zone.

Empirical dependence of the probability of blocks rotations on the diffusion coefficient in a cellular automaton with a Margolus neighbourhood

The paper considers a cellular automaton approach to modeling physical processes, in particular, the diffusion of pulsed periodic gas discharges in plasma. An attempt to determine the dependence of the probability of the block rotation on the diffusion coefficient for a cellular automaton diffusion model with a Margolus neighborhood is describe. Some features of the tensor approach to the implementation of random block cellular automata are described. The results of computer experiments are presented. The analysis of this results indicates that the data from the literature sources differ from the data obtained during the experiment.

A stream cipher algorithm based on 2D coupled map lattice and partitioned cellular automata

The two-dimensional coupled map lattice (2D CML) is a spatiotemporal chaotic model with complex dynamic behavior and has high potential for designing stream cipher. We propose an offset 2D CML model by adding different offsets for each lattice. The offset 2D CML model has better chaotic properties, such as larger Lyapunov exponent (LE) and more uniform chaotic sequences, than the original 2D CML model, which provides a good basis for constructing stream cipher. We combine the offset 2D CML model with the partitioned cellular automata (PCA) and propose a stream cipher algorithm. In our algorithm, the PCA is used to control the extraction of pseudo-random number from the offset 2D CML model, which effectively hides the orbit information of system and enhances the difficulty of attacking chaotic sequences. Moreover, some fast nonlinear transform operations are specially introduced into our algorithm to further improve the complexity and the running speed. Theory analysis and simulation test both confirm that the proposed stream cipher algorithm has excellent statistical performance, high security and computational efficiency. It has great potential for guaranteeing data security in the Internet.

Designing and testing of the computational approach of decorrelating transformation bases construction with the use of partitioning cellular automata

The given paper shows the ability of construction of decorrelating transformation bases, which can be used for digital images compression, by means of cellular automata dynamics. We introduce the construction algorithms of decorrelating transformation bases, generated from evolving states of partitioning cellular automata, which is considered to be the extension of classical model of cellular automaton.

A computation-universal two-dimensional 8-state triangular reversible cellular automaton

A reversible cellular automaton (RCA) is a cellular automaton (CA) whose global function is injective and every configuration has at most one predecessor. Margolus showed that there is a computation-universal two-dimensional 2-state RCA. But his RCA has a non-uniform neighbor, so Morita and Ueno proposed 16-state computation-universal RCA using partitioned cellular automata (PCA). Because PCA can be regarded as a subclass of standard CA, their models have a standard neighbor. In this paper, we show that the number of states of Morita and Ueno's models can be reduced. To decrease the number of states from their models with preserving isotropic and bit-preserving properties, we used a triangular 3-neighbor, and thus an 8-state RCA can be possible. This is the smallest state two-dimensional RCA under the condition of isotropic property in the framework of PCA. We show that our model can simulate basic circuit elements such as unit wires, delay elements, crossing wires, switch gates and inverse switch gates, and it is possible to construct a Fredkin gate by combining these elements. Since Fredkin gate is known to be a universal logic gate, our model has computation-universality.

CHARACTERIZING THE ABILITY OF PARALLEL ARRAY GENERATORS ON REVERSIBLE PARTITIONED CELLULAR AUTOMATA

A PCAAG introduced by Morita and Ueno is a parallel array generator on a partitioned cellular automaton (PCA) that generates an array language (i.e. a set of symbol arrays). A "reversible" PCAAG (RPCAAG) is a backward deterministic PCAAG, and thus parsing of two-dimensional patterns can be performed without backtracking by an "inverse" system of the RPCAAG. Hence, a parallel pattern recognition mechanism on a deterministic cellular automaton can be directly obtained from a RPCAAG that generates the pattern set. In this paper, we investigate the generating ability of RPCAAGs and their subclass. It is shown that the ability of RPCAAGs is characterized by two-dimensional deterministic Turing machines, i.e. they are universal in their generating ability. We then investigate a monotonic RPCAAG (MRPCAAG), which is a special type of an RPCAAG that satisfies monotonic constraint. We show that the generating ability of MRPCAAGs is exactly characterized by two-dimensional deterministic linear-bounded automata.

Cellular automata simulation of the phenomenon of multiple crystallization

The phenomenon of multiple crystallization from supersaturated solutions was simulated. For this simulation the model used is based on partitioning cellular automata (CA) with probabilistic table lookup for the implementation of diffusion and interaction according to diffusion and crystal growth basic equations. Such an approach, which takes into account temperature, crystallographic indexes of crystal surface and local fluctuations describes the problem at a mesoscopic level. This simulates the physical processes of diffusion, nucleation, and aggregation of particles. Results were obtained that are in qualitative agreement with the behavior of the majority of real situation for the: (i) temperature dependence of the crystal solubility; (ii) temperature dependence of the concentration of beginning of crystallization from supersaturated solutions. It was also studied the processes of crystallization at different temperatures and analyzed the behavior of the different parameters involved in crystallization systems: concentration of solution, interfacial energy, mass of crystals and average size of crystal. Finally, the process of crystallization was modeled at several conditions of temperature gradient.

Self-reproduction in a reversible cellular space

We investigate a problem whether self-reproduction is possible in a two-dimensional “reversible” cellular space, and give an affirmative answer. A reversible (or injective) cellular automaton (RCA) is a CA such that every configuration has at most one predecessor. In order to design an RCA we use a framework of partitioned cellular automaton (PCA). A PCA with von Neumann neighborhood is a special type of CA whose cell is divided into five parts. We designed here a reversible PCA SR 8 having 8 states in each part (thus one cell has 8 5 states). In this cellular space, encoding the shape of an object into a “gene” represented by a command sequence, copying the gene, and interpreting the gene to create an object, are all performed reversibly. We show that, by using these operations, various objects can reproduce themselves in a very simple manner.

From quantum cellular automata to quantum lattice gases

A natural architecture for nanoscale quantum computation is that of a quantum cellular automaton. Motivated by this observation, in this paper we begin an investigation of exactly unitary cellular automata. After proving that there can be no nontrivial, homogeneous, local, unitary, scalar cellular automaton in one dimension, we weaken the homogeneity condition and show that there are nontrivial, exactly unitary, partitioning cellular automata. We find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton. This model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the Dirac equation. We describe two generalizations of this automaton, the second of which, to multiple interacting particles, is the correct definition of a quantum lattice gas.

Reversible simulation of one-dimensional irreversible cellular automata

A cellular automaton (CA) is called reversible (or injective) iff its global function is one-to-one. It has been shown by Toffoli that any (irreversible) k-dimensional CA is simulated by a k + 1-dimensional RCA. In this paper, we show that any one-dimensional CA with finite configurations can be simulated by a one-dimensional reversible CA. This is proved by using the framework of partitioned CA (PCA).

PARALLEL GENERATION AND PARSING OF ARRAY LANGUAGES USING REVERSIBLE CELLULAR AUTOMATA

We propose a new system of generating array languages in parallel, based on a partitioned cellular automaton (PCA), a kind of cellular automaton. This system is called a PCA array generator (PCAAG). The characteristic of PCAAG is that a”reversible” version is easily defined. A reversible PCA (RPCA) is a backward deterministic PCA, and we can construct a deterministic “inverse” PCA that undoes the operations of the RPCA. Thus if an array language is generated by an RPCA, it can be parsed in parallel by a deterministic inverse PCA without backtracking. We also define two subclasses of PCAAG, and give examples of them that generate geometrical figures.

Computation-universality of one-dimensional one-way reversible cellular automata

A reversible (or injective) cellular automaton (RCA) is a “backward deterministic” CA, i.e., every configuration of it has at most one predecessor. Reversible systems have been studied to investigate the limitation of inevitable power dissipation in computing processes, and many interesting results have been shown (see e.g. [2-41X As for RCA, Toffoli [9] showed that every (irreversible) k-dimensional CA can be simulated by a k + l-dimensional RCA and thus two-dimensional RCA is computation-universal. In the two-dimensional case, Margolus [5] gave a very simple computation-universal model of 2-state RCA with so-called Margolus neighborhood. On the other hand, Morita and Ueno [8] showed two universal models of two-dimensional 16-state RCA with usual von Neumann neighborhood. In the one-dimensional case, it has been shown by Morita and Harao [6] that a three-neighbor RCA is computation-universal. In this paper, we investigate the computing ability of a one-dimensional two-neighbor (i.e., one-way) RCA. We first investigate a one-dimensional partitioned cellular automaton (PCA), a special subclass of a CA, and show that a three-neighbor RPCA can be simu-