12. [10 bonus points) Let us define an operation truncate, which removes the rightmost symbol from...

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12. [10 bonus points) Let us define an operation truncate, which removes the rightmost symbol from any string. For example, t

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Answer 1

Answer #1

Regular languages are closed under
-> Reversal

If there is an NFA or DFA that accepts a language, then it is regular and vice-versa

We have a DFA, D for language L since L is regular.

So, we have an DFA D' (Initial state A) that is reverse of L

Using D' we can construct a DFA with Initial state A to other states on each of the symbol from alphabet for the first symbol.

Change all symbols in the transitions of A-other states to lambda. We have an NFA now that is reverse of truncate(L)

Since regular languages are closed under reversal
truncate(L) is regular.

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