Theory Automata

Switching and Automata Theory, Santa Monica, California (1970) 194-215. 

Friednan, E. P., "Equivalence Problems in Monadic Recursion Schemes," Proceedings mth Annual Symposium on Switching and Automata Theory, low City, Iowa, 1973, 26-33. 

Hopcroft, John E., Jeffry D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, 1979. 

H. Gutowitz, Cellular Automata Theory and Experiment, MIT Press, Cambridge, MA,... 

Production rules are a formalism commonly used in expert systems but which have their origin in automata theory and formal grammars. Each rule consists of an antecedent-consequent pair, for example ... 

Kain, R. Y., "Automata Theory Machines and Languages", McGraw-Hill, New York, 1972. 

In contrast to the continuous models, the discrete models consider the processes at the level of individual structural elements, e.g. individual fibres, threads or loops, or individual stages of the process. In these models the processes are modelled as a series of states where the transition from one state to another happens with a probability. The underpinning theories for these models are theory of Markov processes (Kemeny and Snell, 1960), queuing theory (Gross et nf, 2008), and finite automata theory (Anderson, 2006 Hopcroft et al., 2007). 

Anderson J A (2006), Automata Theory with Modern Applications, Cambridge, Cambridge University Press. 

Grishanov S A, Cassidy T and Spencer D J (1997a), A model of the loop formation process on the knitting machines using finite automata theory , Appl Math MoifeZ, 21(7), 455-465. 

Pettersson, R Modelling and Verification of Real-Time Systems Using Timed Automata Theory and Practice. PhD thesis. Department of Computer Systems, Uppsala University (February 1999)... 

Hopcroft, J. E., and UUman, J. D. (1979) Introduction to automata theory, languages, and computation, Addison-Wesley, Reading, Mass. 

We chose an automaton model, rather than the traditional control-data flow gr h model [14, IS, 16,17,13], because automata theory gives us powerful algorithms and theorems for the manipulation of control. Much of this powo comes from the clean distinction between behaviw and structure. An automaton is fundamentally defined by its input-ouQnit behavior any state transitirai table which produces the same I/O behavior is an implementation of that automaton. If the machine were defined by its state transition table, it would be difficult to do more with the machine than simply examine it. But since the machine is defined by its I/O behavior, we can perform any transformation on a state transition table which preserves that behavior. Useful transformations in manipulating control include [18] ... 

Zvi Kohavi. Switching and Finite Automata Theory. York, second edition, 1978. 

The label determinism is used in a variety of senses, some of which are seemingly contradictory. Here, we adopt the notion, familiar from automata theory [22], which differs from that in physics, say, of non-stochasticity. One calls a finite-state machine (classical or quantum) deterministic whenever the transition from one state to the next is uniquely determined by the output symbol (or input symbol for recognizers). It is important to realize that a deterministic finite-state machine can still behave stochastically—stochasticity here referring to the positive probability of generating symbols. Once the symbol is determined, though, the transition taken by the machine to the next state is unique. Thus, what is called a stochastic process in dynamical systems theory can be described by a deterministic finite-state generator without contradiction. 

We established a connection between quantum automata theory and quantum dynamics, similar to the way symbolic dynamics connects classical dynamics and automata. By considering the output sequence of a repeatedly measured quantum system as a shift system we foimd quantmn processes that are sofic systems. Taking one quantum system and observing it in one way yields a subshift of finite type. Observing it in a different way yields a (strictly sofic) subshift of infinite type. Consequently, not only the amoimt of memory but also the soficity of a quantum process depend on the means of observation. 

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