Opacity of a finite automaton, method of calculation and the Ising chain

  • Authors:

  • Jia-Yan Yao

  • Affiliations:

  • Department of Mathematics, Nonlinear Science Center, Wuhan University, Wuhan 430072, People's Republic of China

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2003

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Abstract

When a communication system transmits information, inevitably it will produce some noises which disturb the transmitted information. These noises may be caused by some physical or statistical reasons. The study of these exterior factors is very important and we can find in the literature many excellent books and articles about them. However, the most important causes are not exterior but interior ones which come from the internal structure of our communication system. In 1991, Michel Mendès France introduced the notion of opacity of a finite automaton, which is a good intuitive mathematical model for a communication system, and applied it to study the inhomogeneous Ising chain, Since then, opacity becomes an important tool in the study of noises produced during information transmission. In this work, we shall continue our study in opacity theory. More precisely, we shall give a general method to compute the opacity of any given finite automaton. As an application, we shall calculate the opacities of the Ising automata.