Cellular automata simulation of urban dynamics through GPGPU

In recent years, urban models based on Cellular Automata (CA) are becoming increasingly sophisticated and are being applied to real-world problems covering large geographical areas. As a result, they often require extended computing times. However, in spite of the improved availability of parallel computing facilities, the applications in the field of urban and regional dynamics are almost always based on sequential algorithms. This paper makes a contribution toward a wider use in the field of geosimulation of high performance computing techniques based on General-Purpose computing on Graphics Processing Units (GPGPU). In particular, we investigate the parallel speedup achieved by applying GPGPU to a popular constrained urban CA model. The major contribution of this work is in the specific modeling we propose to achieve significant gains in computing time, while maintaining the most relevant features of the traditional sequential model.     

Linear cellular automata and Fischer automata

We study the sizes of minimal finite state machines associated with linear cellular automata. In particular, we construct a class of binary linear cellular automata whose corresponding minimal automata exhibit full exponential blow-up. These cellular automata have Hamming distance 1 to a permutation automaton. Moreover, the corresponding minimal Fischer automata as well as the minimal DFAs have maximal complexity. By contrast, the complexity of higher iterates of a cellular automaton always stays below the theoretical upper bound.     

Sand automata as cellular automata

In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with simple sand automata. We show that the classical definition of nilpotency is not meaningful for sand automata. Then, we introduce the suitable new notion of flattening sand automata. Finally, we prove that this simple dynamical behavior is undecidable.     

污水处理净化过程的三维细胞自动机动态模拟

针对污水处理过程的复杂性、不可重复性和不可再现性等特点,根据活性污泥的净化机理与动力学特性,在Mckinney等人建立的经典活性污泥法动力学模型的基础上,提出了一种模拟活性污泥净化过程的三维格子气细胞自动机模型.该模型的演化规则根据微生物的增殖规律和经典的动力学模型设计,模型通过模拟有机物和微生物的扩散、反应和沉降过程,反应了活性污泥的整个净化过程.对模型进行的仿真实验结果表明:该模型不仅可以复现污水净化过程,而且更直观地刻画了活性污泥法污水处理过程的动态演化行为,直接反映出活性污泥法系统的表观特征.     

On real-time cellular automata and trellis automata

Summary It is shown that f(n)-time one-way cellular automata are equivalent to f(n)-time trellis automata, the real-time one-way cellular automata languages are closed under reversal, the 2n-time one-way cellular automata are equivalent to real-time cellular automata and the latter are strictly more powerful than the real-time one-way cellular automata.This work has been done during the second author's visit at the University of Paris and during both authors' visit at the Institute für Informationsverarbeitung Graz, Austria     

Symmetric cellular automata

A class of cellular automata with permutation-invariant local rules acting on symmetric lattices is considered. In the case of two states, we show that these local rules are nothing else than a generalization of the rules of the game of Life. In view of the symmetry relative to the state renaming, we can further reduce the number of possible automata. For automata with symmetric rules acting on highly symmetric lattices, we can develop efficient algorithms to study their dynamics. Relevant examples are presented.     

Path-bounded three-dimensional finite automata

The comparative study of the computational powers of deterministic and nondeterministic computations is one of the central tasks in complexity theory. This paper investigates the computational power of nondeterministic computing devices with restricted nondeterminism. There are only few results measuring the computational power of restricted nondeterminism. In general, there are three possibilities to measure the amount of nondeterminism in computation. In this paper, we consider the possibility to count the number of different nondeterministic computation paths on any input. In particular, we deal with five-way three-dimensional finite automata with multiple input heads operating on three-dimensional input tapes. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Sequential and cellular graph automata

Labeled graphs of bounded degree, with numbers assigned to the arcs at each node, are called d-graphs. Sequential and cellular d-graph automata are defined, and it is shown that they can simulate each other and are also equivalent to web-bounded automata.     

Non-deterministic cellular automata and languages

We summarize results on non-deterministic cellular language acceptors. The non-determinism is regarded as limited resource. For parallel devices, it is natural to bound the non-determinism in time and/or space. Depending on the length of the input, the number of allowed non-deterministic state transitions as well as the number of non-deterministic cells at all is limited. We centre our attention to real-time, linear-time, and unrestricted-time computations and discuss the computational power of these machines. Speed-up results and the possibility to reduce the non-determinism as well as closure properties of languages acceptable with a constant number of non-deterministic transitions are presented. By considering the relations with context-free languages, several relations between the devices in question are implied. We do not prove these results but we merely draw attention to the big picture and some of the main ideas involved, and open problems for further research.     

“Real-time” equivalence of cellular automata and linear-bounded automata

It is shown that a one-dimensional bounded cellular automaton (BCA) can simulate a linear-bounded automaton (LBA) in essentially real time, and that, conversely, an LBA can simulate a BCA, on an input of length n, in just n transitions of the LBA per BCA transition.     

Cryptography with cellular automata

Cryptography has become a basic requirement in this age of global electronic connectivity to secure data storage and transmission against the possibility of message eavsdropping and electronic fraud. In this article, we describe a single key crypto-graphic system based on one- and two-dimensional non-uniform cellular automata randomizers obtained by artificial evolution. The robustness of the scheme against cryptanalytic attacks is discussed and it is shown that direct cryptanalysis requires an exponentially growing amount of computational resources. The advantage of implementing the proposed scheme in hardware for high-speed operation is also discussed.     

Alternation on cellular automata

In this paper we consider several notions of alternation in cellular automata: non-uniform, uniform and weak alternation. We study relations among these notions and with alternating Turing machines. It is proved that the languages accepted in polynomial time by alternating Turing machines are those accepted by alternating cellular automata in polynomial time for all the proposed alternating cellular automata. In particular, this is true for the weak model where the difference between existential and universal states is omitted for all the cells except the first one. It is proved that real time alternation in cellular automata is strictly more powerful than real time alternation in Turing machines, with only one read-write tape. Moreover, it is shown that in linear time uniform and weak models agree.     

Asynchronous cellular learning automata

Cellular learning automata is a combination of cellular automata and learning automata. The synchronous version of cellular learning automata in which all learning automata in different cells are activated synchronously, has found many applications. In some applications a type of cellular learning automata in which learning automata in different cells are activated asynchronously (asynchronous cellular learning automata) is needed. In this paper, we introduce asynchronous cellular learning automata and study its steady state behavior. Then an application of this new model to cellular networks has been presented.     

Shrinking one-way cellular automata

We investigate cellular automata as acceptors for formal languages. In particular, we consider real-time one-way cellular automata (\(\text{OCA}\)) with the additional property that during a computation any cell of the \(\text{OCA}\) has the ability to dissolve itself, so-called shrinking one-way cellular automata (\(\text{SOCA}\)). It turns out that real-time \(\text{SOCA}\) are more powerful than real-time \(\text{OCA}\), since they can accept certain linear-time \(\text{OCA}\) languages. On the other hand, linear-time \(\text{OCA}\) are more powerful than real-time \(\text{SOCA}\), which is witnessed even by a unary language. Additionally, a construction is provided that enables real-time \(\text{SOCA}\) to accept the reversal of real-time iterative array languages. Finally, restricted real-time \(\text{SOCA}\) are investigated. We distinguish two limitations for the dissolving of cells. One restriction is to bound the total number of cells that are allowed to dissolve by some function. In this case, an infinite strict hierarchy of language classes is obtained. The second restriction is inspired by an approach to limit the amount of nondeterminism in \(\text{OCA}\). Compared with the first restriction, the total number of cells that may dissolve is still unbounded, but the number of time steps at which a cell may dissolve is bounded. The possibility to dissolve is allowed only in the first k time steps, where \(k\ge 0\) is some constant. For this mode of operation an infinite, tight, and strict hierarchy of language classes is obtained as well.     

Identification of probabilistic cellular automata

The identification of probabilistic cellular automata (PCA) is studied using a new two stage neighborhood detection algorithm. It is shown that a binary probabilistic cellular automaton (BPCA) can be described by an integer-parameterized polynomial corrupted by noise. Searching for the correct neighborhood of a BPCA is then equivalent to selecting the correct terms which constitute the polynomial model of the BPCA, from a large initial term set. It is proved that the contribution values for the correct terms can be calculated independently of the contribution values for the noise terms. This allows the neighborhood detection technique developed for deterministic rules in to be applied with a larger cutoff value to discard the majority of spurious terms and to produce an initial presearch for the BPCA neighborhood. A multiobjective genetic algorithm (GA) search with integer constraints is then evolved to refine the reduced neighborhood and to identify the polynomial rule which is equivalent to the probabilistic rule with the largest probability. A probability table representing the BPCA can then be determined based on the identified neighborhood and the deterministic rule. The new algorithm is tested over a large set of one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) BPCA rules. Simulation results demonstrate the efficiency of the new method.     

Entropy of multidimensional cellular automata

Since the topological entropy of a vast class of two-dimensional cellular automata (CA) is infinite, of interest is the possibility to renormalize it so that to obtain a positive finite value. We find the asymptotics of the information function of a multidimensional CA and, accordingly, introduce the renormalized topological entropy as a coefficient of this asymptotics. We describe some properties of the introduced quantity, in particular, its positivity for CA of the type of “The Game of Life.” Also, we give an example of an explicit evaluation of this parameter for a particular cellular automaton.     

Computational classification of cellular automata

We discuss attempts at the classification of cellular automata, in particular with a view towards decidability. We will see that a large variety of properties relating to the short-term evolution of configurations are decidable in principle, but questions relating to the long-term evolution are typically undecidable. Even in the decidable case, computational hardness poses a major obstacle for the automatic analysis of cellular automata.     

Identification of Nonstationary Cellular Automata

The principal feature of nonstationary cellular automata(NCA) is that a local transitiol rule of each cell is changed at each time step depending on neighborhood configuration at previous time step.The identification problem for NCA is extraction of local transition rules and the establishment of mechanism for changing these rules using sequence of NCA configurations.We present serial and parallel algorithms for identification of NCA.