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In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical…
A number-conserving cellular automaton is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modelization of the physical…
Recurrent transducer models have emerged as a promising solution for speech recognition on the current and next generation smart devices. The transducer models provide competitive accuracy within a reasonable memory footprint alleviating…
We present a parallel implementation of cellular automata to simulate chemical reactions on surfaces. The scaling of the computer time with the number of processors for this parallel implementation is quite close to the ideal T/P, where T…
Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also triggered great interest in the time series community. Among multiple advantages of Transformers, the ability to…
We define a cellular automaton where a resting cell excites if number of its excited neighbours belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbours in the cell's…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…
In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical…
State of the art sequence-to-sequence models for large scale tasks perform a fixed number of computations for each input sequence regardless of whether it is easy or hard to process. In this paper, we train Transformer models which can make…
Cellular automata are arrays of finite state machines that can exist in a finite number of states. These machines update their states simultaneously based on specific local rules that govern their interactions. This framework provides a…
Vertex models represent confluent tissue by polygonal or polyhedral tilings of space, with the individual cell interacting via force laws that depend on both the geometry of the cells and the topology of the tessellation. This dependence on…
Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…
In three spatial dimensions, communication channels are free to pass over or under each other so as to cross without intersecting; in two dimensions, assuming channels of strictly positive thickness, this is not the case. It is natural,…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
Thermal noise in a cellular automaton refers to a random perturbation to its function which eventually leads this automaton to an equilibrium state controlled by a temperature parameter. We study the 1-dimensional majority-3 cellular…
In this paper, we present a novel algorithm to optimize the design of Reservoir Computing using Cellular Automata models for time series applications. Besides selecting the models' hyperparameters, the proposed algorithm particularly solves…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
The work is concerned with the trade-offs between the dimension and the time and space complexity of computations on nondeterministic cellular automata. It is proved, that 1). Every NCA $\Cal A$ of dimension $r$, computing a predicate $P$…
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…