On two-way communication in cellular automata with a fixed number of cells

The effect of adding two-way communication to k cells one-way cellular automata (kC-OCAs) on their size of description is studied. kC-OCAs are a parallel model for the regular languages that consists of an array of k identical deterministic finite automata (DFAs), called cells, operating in parallel. Each cell gets information from its right neighbor only. In this paper, two models with different amounts of two-way communication are investigated. Both models always achieve quadratic savings when compared to DFAs. When compared to a one-way cellular model, the result is that minimum two-way communication can achieve at most quadratic savings whereas maximum two-way communication may provide savings bounded by a polynomial of degree k

Communication Complexity and Intrinsic Universality in Cellular Automata

The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce necessary conditions for a cellular automaton to be "universal", according to a precise notion of simulation, related both to the dynamics of cellular automata and to their computational power. This notion of simulation relies on simple operations of space-time rescaling and it is intrinsic to the model of cellular automata. Intrinsinc universality, the derived notion, is stronger than Turing universality, but more uniform, and easier to define and study. Our approach builds upon the notion of communication complexity, which was primarily designed to study parallel programs, and thus is, as we show in this article, particulary well suited to the study of cellular automata: it allowed to show, by studying natural problems on the dynamics of cellular automata, that several classes of cellular automata, as well as many natural (elementary) examples, could not be intrinsically universal

On the descriptional complexity of iterative arrays

The descriptional complexity of iterative arrays (lAs) is studied. Iterative arrays are a parallel computational model with a sequential processing of the input. It is shown that lAs when compared to deterministic finite automata or pushdown automata may provide savings in size which are not bounded by any recursive function, so-called non-recursive trade-offs. Additional non-recursive trade-offs are proven to exist between lAs working in linear time and lAs working in real time. Furthermore, the descriptional complexity of lAs is compared with cellular automata (CAs) and non-recursive trade-offs are proven between two restricted classes. Finally, it is shown that many decidability questions for lAs are undecidable and not semidecidable

Visual Spike-based Convolution Processing with a Cellular Automata Architecture

this paper presents a first approach for implementations which fuse the Address-Event-Representation (AER) processing with the Cellular Automata using FPGA and AER-tools. This new strategy applies spike-based convolution filters inspired by Cellular Automata for AER vision processing. Spike-based systems are neuro-inspired circuits implementations traditionally used for sensory systems or sensor signal processing. AER is a neuromorphic communication protocol for transferring asynchronous events between VLSI spike-based chips. These neuro-inspired implementations allow developing complex, multilayer, multichip neuromorphic systems and have been used to design sensor chips, such as retinas and cochlea, processing chips, e.g. filters, and learning chips. Furthermore, Cellular Automata is a bio-inspired processing model for problem solving. This approach divides the processing synchronous cells which change their states at the same time in order to get the solution.Ministerio de Educación y Ciencia TEC2006-11730-C03-02Ministerio de Ciencia e Innovación TEC2009-10639-C04-02Junta de Andalucía P06-TIC-0141

Sublinearly space bounded iterative arrays

Iterative arrays (IAs) are a, parallel computational model with a sequential processing of the input. They are one-dimensional arrays of interacting identical deterministic finite automata. In this note, realtime-lAs with sublinear space bounds are used to accept formal languages. The existence of a proper hierarchy of space complexity classes between logarithmic anel linear space bounds is proved. Furthermore, an optimal spacc lower bound for non-regular language recognition is shown. Key words: Iterative arrays, cellular automata, space bounded computations, decidability questions, formal languages, theory of computatio

On one-way cellular automata with a fixed number of cells

We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA

Descriptional complexity of cellular automata and decidability questions

We study the descriptional complexity of cellular automata (CA), a parallel model of computation. We show that between one of the simplest cellular models, the realtime-OCA. and "classical" models like deterministic finite automata (DFA) or pushdown automata (PDA), there will be savings concerning the size of description not bounded by any recursive function, a so-called nonrecursive trade-off. Furthermore, nonrecursive trade-offs are shown between some restricted classes of cellular automata. The set of valid computations of a Turing machine can be recognized by a realtime-OCA. This implies that many decidability questions are not even semi decidable for cellular automata. There is no pumping lemma and no minimization algorithm for cellular automata