Name
Abstract | ||
|---|---|---|
Global dynamics of a non-linear Cellular Automaton (CA), is, in general irregular, asymmetric and unpredictable as opposed to that of a linear CA, which is highly systematic and tractable. In this paper, efforts have been made to systematize non-linear CA evolutions in the light of Boolean derivatives and Jacobian matrices. A few new theorems on Hamming Distance between Boolean functions as well as on Jacobian matrices of cellular automata are proposed and proved. Moreover, a classification of Boolean functions based on the nature of deviation from linearity has been suggested with a view to grouping them together to classes/subclasses such that the members of a class/subclass satisfy certain similar properties. Next, an error vector, which cannot be captured by the Jacobian matrix, is identified and systematically classified. This leads us to the concept of modified Jacobian matrix whereby a quasi-affine representation of a non-linear cellular automaton is introduced. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1016/j.camwa.2008.11.012 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
boolean function,non-linear ca evolution,boolean derivative,global dynamic,wolfram’s naming scheme,linear and affine functions,certain similar property,linear ca,hamming distance,algebraic normal form,jacobian matrix,cellular automaton,state transition diagram,non-linear cellular automaton,error function,boolean functions,modified jacobian matrix,cellular automata,satisfiability | Boolean function,Boolean network,Discrete mathematics,Cellular automaton,Mathematical optimization,Mathematical analysis,Parity function,Reversible cellular automaton,Block cellular automaton,Stochastic cellular automaton,Boolean expression,Mathematics | Journal |
Volume | Issue | ISSN |
57 | 8 | Computers and Mathematics with Applications |
Citations | PageRank | References |
8 | 1.09 | 1 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Pabitra Pal Choudhury | 1 | 69 | 28.27 |
| Sudhakar Sahoo | 2 | 51 | 13.13 |
| Mithun Chakraborty | 3 | 42 | 12.16 |
| Subir Kumar Bhandari | 4 | 8 | 1.43 |
| Amita Pal | 5 | 18 | 4.84 |