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As we know, the definition of 'finite state automata' is: enter image description here

Then we have this finite state automat described as: enter image description here

Then we have the conclusion: enter image description here

Question is : Instead of accept an empty string, what if the automat first read string is '2', which is not belong to the alphabet(0,1) of this automata. will this automata still go to accept state?

pics quoted from book <Introduction to the Theory of Computation>

Anonemous
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  • Undefined behaviour - it's not part of the definition of the object what it should do when it encounters inputs outside its alphabet. This is analogous to division by zero. To help enlighten why this is, consider the question, "What does it matter if M3 is fed the input '2'?" Does it lead to any theorems if it halts? If it runs forever? If it rejects? If it accepts? Does it give you any insight into the mathematics of DFAs to think about how it reads the input '2'? The answer is no, it doesn't really matter. The insights are in the parts that are specified, not the parts that aren't defined. – Welbog May 22 '19 at 13:00

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When a machine is defined, one of its items is the alphabet (second one in your definition). We are not allowed to test our machine outside the scope of the alphabet. Therefore, all strings of L (accepted strings) and L-bar (rejected strings) should come out of Sigma-star.

Ahmad
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