Please solve problem b.

Describe and Justify the proofs

(b-dfa) Let us define an operation truncate, which removes the rightmost symbol from any string. For example, truncate (aaaba) is aaab. The operation can be extended to languages by

truncate (L) = {truncate (w) : w L} .

Show how, given a dfa for any regular language L, one can construct a dfa for truncate (L). From this, prove that if L is a regular language not containing , then truncate (L) is also regular.

(a-nfa) From a language L, we create a new language, chopleft (L), by removing the leftmost symbol of every string in L. Specifically, chopleft (L) = {w : VW L, with |v= 1} . Show that if L is regular, then chopleft (L) is also regular. (b-dfa) Let us define an operation truncate, which removes the rightmost symbol from any string. For example, truncate (aaaba) is aaab. The operation can be extended to languages by truncate (L) = {truncate (w): we L} . Show how, given a dfa for any regular language L, one can construct a dfa for truncate (L). From this, prove that if L is a regular language not containing 1, then truncate (L) is also regular