Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States
Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the propertie...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2011/605098 |
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| author | Pabitra Pal Choudhury Sudhakar Sahoo Mithun Chakraborty |
| author_facet | Pabitra Pal Choudhury Sudhakar Sahoo Mithun Chakraborty |
| author_sort | Pabitra Pal Choudhury |
| collection | DOAJ |
| description | Dynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules. |
| format | Article |
| id | doaj-art-21ceab5805094cd5874b59d703ba03cd |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-21ceab5805094cd5874b59d703ba03cd2025-02-03T06:08:34ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252011-01-01201110.1155/2011/605098605098Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant StatesPabitra Pal Choudhury0Sudhakar Sahoo1Mithun Chakraborty2Applied Statistics Unit, Indian Statistical Institute, Kolkata 700108, IndiaDepartment of Computer Science, Institute of Mathematics and Applications, Andharua, Bhubaneswar 751003, IndiaDepartment of Computer Science, Rensselaer Polytechnic Institute, Troy, NY 12180-3590, USADynamics of a nonlinear cellular automaton (CA) is, in general asymmetric, irregular, and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable, primarily due to the presence of a matrix handle. In this paper, we present a novel technique of studying the properties of the State Transition Diagram of a nonlinear uniform one-dimensional cellular automaton in terms of its deviation from a suggested linear model. We have considered mainly elementary cellular automata with neighborhood of size three, and, in order to facilitate our analysis, we have classified the Boolean functions of three variables on the basis of number and position(s) of bit mismatch with linear rules. The concept of deviant and nondeviant states is introduced, and hence an algorithm is proposed for deducing the State Transition Diagram of a nonlinear CA rule from that of its nearest linear rule. A parameter called the proportion of deviant states is introduced, and its dependence on the length of the CA is studied for a particular class of nonlinear rules.http://dx.doi.org/10.1155/2011/605098 |
| spellingShingle | Pabitra Pal Choudhury Sudhakar Sahoo Mithun Chakraborty Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States International Journal of Mathematics and Mathematical Sciences |
| title | Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States |
| title_full | Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States |
| title_fullStr | Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States |
| title_full_unstemmed | Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States |
| title_short | Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States |
| title_sort | characterization of the evolution of nonlinear uniform cellular automata in the light of deviant states |
| url | http://dx.doi.org/10.1155/2011/605098 |
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