Regular Languages Finite Automata

EXAMPLE Consider an automaton M with alphabet A = 0,1), state space E = cti,CT2,(73,CT4 and transition rule 4 given by 

The computational capabilities of finite automata are actually very limited. Consider, for example, the problem of constructing an arithmetic expression parser . 

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Given an automaton M that starts in state CTi, and any finite string s A, a, s) will represent the final output state that J<4 will enter after having processed s, one symbol at a time, from left to right. J<4 is said to accept the word s if ai,s) E the word s is rejected if and only if it is not accepted. Finally, we may define the language C JA) accepted by M as the set of all words s A that are accepted by Ad. A language C is called regular if there is a finite automaton Ad that accepts it. 

We have described the activity of a finite automaton which accepts the infinite regular language of the general configurations types (of the configurations of the observed machine TM). They are the words of the infinite length and having the form... 

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