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Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
The complexity of cellular automata is traditionally measured by their computational capacity. However, it is difficult to choose a challenging set of computational tasks suitable for the parallel nature of such systems. We study the…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
We consider the computational complexity of tree transducers, depending on their separable sets of input variables.
Parallel algorithms for solving any image processing task is a highly demanded approach in the modern world. Cellular Automata (CA) are the most common and simple models of parallel computation. So, CA has been successfully used in the…
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We…
A commonly used model for fault-tolerant computation is that of cellular automata. The essential difficulty of fault-tolerant computation is present in the special case of simply remembering a bit in the presence of faults, and that is the…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
While there has been a keen interest in studying computation at the edge of chaos for dynamical systems undergoing a phase transition, this has come under question for cellular automata. We show that for continuously deformed cellular…
Computing the configuration of any one-dimensional cellular automaton at generation $n$ can be accelerated by constructing and running a composite rule with a radius proportional to $\log n$. The new automaton is the original one, but with…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
We introduce a novel framework of reservoir computing, that is capable of both connectionist machine intelligence and symbolic computation. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto…
In the paper I sketch a theory of massively parallel proofs using cellular automata presentation of deduction. In this presentation inference rules play the role of cellular-automatic local transition functions. In this approach we…
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…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but…
In this paper, we present the simulation of a simple, yet significantly powerful, sequential model by cellular automata. The simulated model is called oblivious multi-head one-way finite automata and is characterized by having its heads…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…