scholarly journals Characterization of the Evolution of Nonlinear Uniform Cellular Automata in the Light of Deviant States

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Pabitra Pal Choudhury ◽  
Sudhakar Sahoo ◽  
Mithun Chakraborty
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Boolean Functions ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
One Dimensional ◽  
State Transition Diagram ◽  
Linear Rule

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.

The State Transition Diagram

2012 ◽  
pp. 153-157
Author(s):  
Saul Greenberg ◽  
Sheelagh Carpendale ◽  
Nicolai Marquardt ◽  
Bill Buxton
Keyword(s):  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
State Transition Diagram

TEST SCENARIO GENERATION BASED ON FORMAL SPECIFICATION AND USAGE PROFILE

2000 ◽  
Vol 10 (02) ◽  
pp. 185-201 ◽  
Author(s):  
KAI H. CHANG ◽  
SHIH-SUNG LIAO ◽  
RICHARD CHAPMAN ◽  
CHUN-YU CHEN
Keyword(s):  
Formal Specification ◽  
State Transition ◽  
Object Oriented ◽  
The State ◽  
State Model ◽  
Scenario Generation ◽  
Formal Specifications ◽  
Test Scenario ◽  
Transition Diagram ◽  
State Transition Diagram

This paper presents a method for test scenario generation based on formal specifications and usage profiles. It is a major component of a framework for testing object-oriented programs. In this framework, the requirements of a software system are formally specified. The anticipated application of the system is expressed in a usage profile, which is a state model that indicates the dynamic behavior of the system and execution probabilities for the behaviors. The state model is used as a guide to derive the anticipated operation scenarios. An enhanced state transition diagram is used to represent the state model, which incorporates hierarchy, usage and parameter information. Since the number of feasible scenarios can be extremely large, probability and importance criteria are used to select the most probable and important scenarios.

Definition and Application of a Five-Parameter Characterization of One-Dimensional Cellular Automata Rule Space

2001 ◽  
Vol 7 (3) ◽  
pp. 277-301 ◽  
Author(s):  
Gina M. B. Oliveira ◽  
Pedro P. B. de Oliveira ◽  
Nizam Omar
Keyword(s):  
Phase Transition ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Dynamic Behavior ◽  
Discrete Dynamical Systems ◽  
Transition Diagram ◽  
One Dimensional ◽  
Rule Space ◽  
Spatially Extended

Cellular automata (CA) are important as prototypical, spatially extended, discrete dynamical systems. Because the problem of forecasting dynamic behavior of CA is undecidable, various parameter-based approximations have been developed to address the problem. Out of the analysis of the most important parameters available to this end we proposed some guidelines that should be followed when defining a parameter of that kind. Based upon the guidelines, new parameters were proposed and a set of five parameters was selected; two of them were drawn from the literature and three are new ones, defined here. This article presents all of them and makes their qualities evident. Then, two results are described, related to the use of the parameter set in the Elementary Rule Space: a phase transition diagram, and some general heuristics for forecasting the dynamics of one-dimensional CA. Finally, as an example of the application of the selected parameters in high cardinality spaces, results are presented from experiments involving the evolution of radius-3 CA in the Density Classification Task, and radius-2 CA in the Synchronization Task.

STRUCTURAL PRINCIPLES FOR COMPLEX DYNAMICS IN GLASS NETWORKS

2011 ◽  
Vol 21 (01) ◽  
pp. 237-254 ◽  
Author(s):  
LINGHONG LU ◽  
RODERICK EDWARDS
Keyword(s):  
Gene Networks ◽  
Regulatory Networks ◽  
State Transition ◽  
Complex Dynamics ◽  
Piecewise Linear ◽  
Expression Patterns ◽  
The State ◽  
Complex Behavior ◽  
Transition Diagram ◽  
State Transition Diagram

Gene-regulatory networks are potentially capable of more complex behavior than convergence to a stationary state, or even cycling through a simple sequence of expression patterns. The analysis of qualitative dynamics for these networks is facilitated by using piecewise-linear equations and its state transition diagram (an n-dimensional hypercube, in the case of n genes with a single effective threshold for the protein product of each). Our previous work has dealt with cycles of states in the state transition diagram that allow periodic solutions. Here, we study a particular kind of figure-8 pattern in the state transition diagram and determine conditions that allow complex behavior. Previous studies of complex behavior, such as chaos, in such networks have dealt only with specific examples. Our approach allows an appreciation of the design principles that give rise to complex dynamics, which may have application in assessing the dynamical possibilities of gene networks with poorly known parameters, or for synthesis or control of gene networks with complex behavior.

scholarly journals Simplification of State Transition Diagrams in Average Unavailability Analysis by Using Generalized Perturbation Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
R. C. Vicente ◽  
F. C. Silva ◽  
P. F. Frutuoso e Melo ◽  
A. C. M. Alvim
Keyword(s):  
Perturbation Theory ◽  
System Reliability ◽  
State Transition ◽  
The State ◽  
Transition Diagram ◽  
State Transition Diagram ◽  
Component Systems ◽  
Generalized Perturbation Theory ◽  
Integral Quantity ◽  
The Mean

Safety analysis studies in nuclear engineering, more specifically system reliability, usually handle a great number of components, so that computational difficulties may arise. To face the problem of many component systems a method for simplifying the state transition diagram in Markovian reliability analyses has been proposed, using the edges which can be cut, since these latter have a smaller influence on system failure probability. In order to extend the application of GPT (Generalized Perturbation Theory), this work uses GPT formalism to reduce the number of states in a transition diagram, not considering the state probability as the integral quantity of interest, but the mean system unavailability instead. Therefore, after simplifying the original diagram, the mean unavailability for the new system was calculated and the results were very close to those of the original diagram integral quantity (giving a relative error of about 2%), showing that the proposed simplification is quite reasonable and simple to apply.

Synthesis of Scalable Single Length Cycle, Single Attractor Cellular Automata in Linear Time

2021 ◽  
Vol 30 (3) ◽  
pp. 415-439
Author(s):  
Bidesh Chakraborty ◽  
◽  
Mamata Dalui ◽  
Biplab K. Sikdar ◽  
◽  
...  
Keyword(s):  
Cellular Automata ◽  
Linear Time ◽  
Analytical Framework ◽  
Constant Time ◽  
M Cell ◽  
Transition Diagram ◽  
Arbitrary Length ◽  
Attractor State ◽  
One Dimensional ◽  
State Transition Diagram

This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n+1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n+m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.

The Study of the Multi-Sensors’ Reliability on the AMB System of HTR-10GT

2014 ◽  
Author(s):  
Yan Zhou ◽  
Ni Mo ◽  
ZhenGang Shi ◽  
GuoJun Yang
Keyword(s):  
Transition Matrix ◽  
State Transition ◽  
The State ◽  
Measurement Unit ◽  
Active Magnetic Bearings ◽  
Transition Diagram ◽  
Single Degree ◽  
Speed Sensor ◽  
State Transition Diagram ◽  
Amb System

This article uses the Markov process to analyze the displacement redundant unit on the active magnetic bearings (AMB) system in HTR-10GT, especially on the aspects of the reliability, redundancy and maintenance issues. The reliability mathematical model is established, and the state transition diagram and the state transition matrix are deduced under the different conditions, furthermore the expression on reliability of the displacement redundant sensors is given. According to the different failure rate of single degree speed sensor, the curve about the measurement unit reliability versus time is calculated. The method mentioned above provides a new and practical approach to improve the reliability of the system and to optimize the displacement measurement redundant unit, which also can to be as a guiding role for the fault diagnosis of system.

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