Showing papers on "Continuous automaton published in 2016"
TL;DR: It is shown that given simple, periodic inputs, chemical reactions and diffusion can reliably emulate the dynamics of a deterministic cellular automaton, and can therefore be programmed to produce a wide range of complex, discrete dynamics.
Abstract: Chemical reactions and diffusion can produce a wide variety of static or transient spatial patterns in the concentrations of chemical species. Little is known, however, about what dynamical patterns of concentrations can be reliably programmed into such reaction---diffusion systems. Here we show that given simple, periodic inputs, chemical reactions and diffusion can reliably emulate the dynamics of a deterministic cellular automaton, and can therefore be programmed to produce a wide range of complex, discrete dynamics. We describe a modular reaction---diffusion program that orchestrates each of the fundamental operations of a cellular automaton: storage of cell state, communication between neighboring cells, and calculation of cells' subsequent states. Starting from a pattern that encodes an automaton's initial state, the concentration of a "state" species evolves in space and time according to the automaton's specified rules. To show that the reaction---diffusion program we describe produces the target dynamics, we simulate the reaction---diffusion network for two simple one-dimensional cellular automata using coupled partial differential equations. Reaction---diffusion based cellular automata could potentially be built in vitro using networks of DNA molecules that interact via branch migration processes and could in principle perform universal computation, storing their state as a pattern of molecular concentrations, or deliver spatiotemporal instructions encoded in concentrations to direct the behavior of intelligent materials.
36 citations
05 Sep 2016
TL;DR: By slightly relaxing the assumptions on the output specification, this paper can identify a rich family of rules solving the density classification problem in the context of Continuous Cellular Automata.
Abstract: In this paper, we discuss the well-known density classification problem in the context of Continuous Cellular Automata, and recall that this problem cannot be solved in the classical sense. Yet, by slightly relaxing the assumptions on the output specification, we can identify a rich family of rules solving the problem.
7 citations
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TL;DR: In this article, it was shown that if a connected reversible automaton has a prime number of states, it cannot generate an infinite Burnside group, even when the automaton is not reversible.
Abstract: The simplest example of an infinite Burnside group arises in the class of automaton groups. However there is no known example of such a group generated by a reversible Mealy automaton. It has been proved that, for a connected automaton of size at most~3, or when the automaton is not bireversible, the generated group cannot be Burnside infinite. In this paper, we extend these results to automata with bigger stateset, proving that, if a connected reversible automaton has a prime number of states, it cannot generate an infinite Burnside group.
6 citations
TL;DR: In this article, a model for chimera states is presented, which is based on a cellular automata and the majority rule, and it is shown that the system spontaneously splits into stable domains separated by static boundaries, ones synchronously oscillating and others incoherent.
Abstract: A minimalistic model for chimera states is presented. The model is a cellular automaton (CA) which depends on only one adjustable parameter, the range of the nonlocal coupling, and is built from elementary cellular automata and the majority (voting) rule. This suggests the universality of chimera-like behavior from a new point of view: Already simple CA rules based on the majority rule exhibit this behavior. After a short transient, we find chimera states for arbitrary initial conditions, the system spontaneously splitting into stable domains separated by static boundaries, ones synchronously oscillating and the others incoherent. When the coupling range is local, nontrivial coherent structures with different periodicities are formed.
6 citations
11 Jul 2016
TL;DR: A theoretical model of DNA chemical reaction-diffusion network capable of performing a simple cellular automaton based on well-characterized enzymatic bistable switch, which indicates that the model evolves as expected both in space and time from initial conditions.
Abstract: We introduce a theoretical model of DNA chemical reaction-diffusion network capable of performing a simple cellular automaton. The model is based on well-characterized enzymatic bistable switch that was reported to work in vitro. Our main purpose is to propose an autonomous, feasible, and macro DNA system for experimental implementation.
As a demonstration, we choose a maze-solving cellular automaton. The key idea to emulate the automaton by chemical reactions is assuming a space discretized by hydrogel capsules which can be regarded as cells. The capsule is used both to keep the state uniform and control the communication between neighboring capsules.
Simulations under continuous and discrete space are successfully performed. The simulation results indicate that our model evolves as expected both in space and time from initial conditions. Further investigation also suggests that the ability of the model can be extended by changing parameters. Possible applications of this research include pattern formation and a simple computation. By overcoming some experimental difficulties, we expect that our framework can be a good candidate to program and implement a spatio-temporal chemical reaction system.
6 citations
TL;DR: This work introduces a novel method for creating behaviors in cellular automata: optimizing the topology of the cellular substrate while maintaining a single simple update rule and provides insights towards the study of morphological computation and embodied cognition.
5 citations
01 Nov 2016
TL;DR: This paper focuses on the case the authors call finite NCCA when states are non-negative integers, and the total sum is finite, and constructed a radius 1 universal FNCCA by simulating register machines with two registers.
Abstract: A number-conserving cellular automaton (NCCA) 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 particle-based modeling of the physical conservation law of mass. In this paper we focus on the case we call finite NCCA when states are non-negative integers, and the total sum is finite. In spite of the strong constraint, we constructed a radius 1 universal FNCCA by simulating register machines with two registers. We also consider the particle complexity in the case of large (but finite) radius, and constructed a universal FNCCA with only five particles.
5 citations
TL;DR: The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained and the results of the simulation experiments with the obtained algorithm on standard test functions are provided.
Abstract: This article is devoted to the application of the cellular automata mathematical apparatus to the problem of continuous optimization. The cellular automaton with an objective function is introduced as a new modification of the classic cellular automaton. The algorithm of continuous optimization, which is based on dynamics of the cellular automaton having the property of geometric symmetry, is obtained. The results of the simulation experiments with the obtained algorithm on standard test functions are provided, and a comparison between the analogs is shown.
4 citations
TL;DR: In this paper, the authors propose a criterion for testing the reversibility of a multidimensional linear cellular automaton under null boundary condition and an algorithm for the computation of its reverse, if it exists.
Abstract: While the reversibility of multidimensional cellular automata is undecidable and there exists a criterion for determining if a multidimensional linear cellular automaton is reversible, there are only a few results about the reversibility problem of multidimensional linear cellular automata under boundary conditions. This work proposes a criterion for testing the reversibility of a multidimensional linear cellular automaton under null boundary condition and an algorithm for the computation of its reverse, if it exists. The investigation of the dynamical behavior of a multidimensional linear cellular automaton under null boundary condition is equivalent to elucidating the properties of block Toeplitz matrix. The proposed criterion significantly reduce the computational cost whenever the number of cells or the dimension is large; the discussion can also apply to cellular automata under periodic boundary condition with a minor modification.
3 citations
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TL;DR: In this paper, it was shown that a linear cellular automata is pre-injective if and only if its adjoint is surjective, which is the same as the notion of adjoint cellular automaton.
Abstract: We consider linear cellular automata on groups, introduce a notion of adjoint cellular automaton, and prove that a linear cellular automaton is pre-injective if and only if its adjoint is surjective.
In this manner, and relying on a previous construction (for arbitrary non-amenable group $G$ and field $k$) of a pre-injective, non-surjective linear cellular automaton, we produce for arbitrary non-amenable group $G$ and field $k$ a non-pre-injective, surjective linear cellular automaton. This answers positively Open Problem (OP-14) in Ceccherini-Silberstein and Coornaert's monograph "Cellular Automata and Groups".
2 citations
19 Dec 2016
TL;DR: The purpose of the present work is to introduce and study the concept of minimal deterministic automaton with rough output which recognizes the given rough languages using two concepts based on Myhill-Nerode’s theory and derivatives of the givenrough language.
Abstract: The purpose of the present work is to introduce and study the concept of minimal deterministic automaton with rough output which recognizes the given rough languages. Specifically, we use two concepts for such construction, one is based on Myhill-Nerode’s theory and the other is on the basis of derivatives of the given rough language. Lastly, we discuss monoid representations of the given rough languages.
01 Nov 2016
TL;DR: A novel BCA based on a conventional ACA, which employs a smaller number of rules as compared to the previous model, is proposed, capable of universal computing which might demonstrate the crucial role of signal random fluctuation for reducing the complexity of universal ACAs.
Abstract: A Brownian cellular automaton (BCA) is an asynchronous cellular automaton (ACA) in which the local configurations representing signals may fluctuate randomly in the cell space. The random fluctuation of signals enables effective stochastic search to conduct computation, which can actually result in the decreased complexity of BCAs. This paper proposes a novel BCA based on a conventional ACA, which employs a smaller number of rules as compared to the previous model. This BCA is capable of universal computing which might demonstrate the crucial role of signal random fluctuation for reducing the complexity of universal ACAs.
TL;DR: For fuzzy linear automaton the method constructing of generalized synchronization sequences that are optimized according to various criteria are proposed, assuming that the fuzziness inherent in the description of law of the automaton functioning.
Abstract: For fuzzy linear automaton the method constructing of generalized synchronization sequences that are optimized according to various criteria are proposed. It is assumed that the fuzziness inherent in the description of law of the automaton functioning.
05 Sep 2016
TL;DR: A 3-state asynchronous CA that requires merely two transition rules to achieve computational universality is presented, achieved by embedding Priese’s delay-insensitive circuit elements on the cell space of a so-called Brownian CA.
Abstract: This paper presents a 3-state asynchronous CA that requires merely two transition rules to achieve computational universality. This universality is achieved by embedding Priese’s delay-insensitive circuit elements, called the E-element and the K-element, on the cell space of a so-called Brownian CA, which is an asynchronous CA containing local configurations that conduct a random walk in the circuit topology.
01 Oct 2016
TL;DR: A new WFCSR automaton which enhances the traditional matrix representation by incorporating α-mask and/or β-mask operations on certain blocks (or words) of WFC SR automaton can be adopted as a basic primitive to design any pseudo random number generator or stream cipher for cryptographic applications.
Abstract: Feedback with carry shift registers (FCSRs) have been proposed as a promising alternate to the Linear feedback shift registers (LFSRs) in recent years. An approach based on traditional matrix representation has been proposed to design a Word oriented FCSR (WFCSR) automaton in [2], [3]. This automaton always generates a fixed l-sequence, which is not desired for some cryptographic applications. In this paper, we present a new WFCSR automaton which enhances the traditional matrix representation by incorporating α-mask and/or β-mask operations on certain blocks (or words) of WFCSR automaton. By applying different α-mask and/or β-mask on certain blocks (or words) of WFCSR automaton, we can generate multiple l-sequences without changing its structure. We can use the proposed approach to design WFCSR automaton in Fibonacci, Galois and Ring representations. The proposed WFCSR automaton can be adopted as a basic primitive to design any pseudo random number generator or stream cipher for cryptographic applications.
05 Sep 2016
TL;DR: This paper addresses the problem of regional controllability of cellular automata via boundary actions, i.e., the characteristics of a cellular automaton rule are investigated so that it can be controlled inside a given region only acting on the value of sites at its boundaries.
Abstract: An interesting problem in extended physical systems is that of the regional control, i.e., how to add a suitable control at the boundary or inside a region of interest so that the state of such region is near to a desired one. Many physical problems are modelled by means of cellular automata. It is therefore important to port control concepts to this discrete world. In this paper we address the problem of regional controllability of cellular automata via boundary actions, i.e., we investigate the characteristics of a cellular automaton rule so that it can be controlled inside a given region only acting on the value of sites at its boundaries.
20 Oct 2016
TL;DR: It is shown that using the Infinite Unit Axiom, the number of configurations that follow a given configuration, under the forward iterations of cellular automaton maps, can now be computed and hence a classification scheme developed bas...
Abstract: This paper proposes an application of the Infinite Unit Axiom and grossone, introduced by Yaroslav Sergeyev (see [7] - [12]), to the development and classification of one and two-dimensional cellular automata. By the application of grossone, new and more precise nonarchimedean metrics on the space of definition for one and two-dimensional cellular automata are established. These new metrics allow us to do computations with infinitesimals. Hence configurations in the domain space of cellular automata can be infinitesimally close (but not equal). That is, they can agree at infinitely many places. Using the new metrics, open disks are defined and the number of points in each disk computed. The forward dynamics of a cellular automaton map are also studied by defined sets. It is also shown that using the Infinite Unit Axiom, the number of configurations that follow a given configuration, under the forward iterations of cellular automaton maps, can now be computed and hence a classification scheme developed bas...
TL;DR: By expanding the range of initial conditions considered to include complex backgrounds, code 1599 can produce patterns that are entirely different from its ordinary structure, but similar or even structurally identical to some elementary cellular automata rules.
Abstract: Code 1599 is a cellular automaton rule that produces complex patterns that resemble the phenomenon of free will under simple initial conditions. However, by expanding the range of initial conditions considered to include complex backgrounds, we find that code 1599 can produce patterns that are entirely different from its ordinary structure, but similar or even structurally identical to some elementary cellular automata rules.