A finite state machine with the following state table has a single input $$X$$ and a single out $$Z$$.

If the initial state is unknown, then the shortest input sequence to reach the final state $$C$$ is here, since initial make unknown $$m$$ $$10$$ input we can each final state $$C$$ with shortest path.

Which of the following definitions below generates the same language as $$L$$
Where $$L = {\left\{ x \right.^n}{y^n}\left| {n \ge \left. 1 \right\}} \right.$$
i) $$\,\,E \to xEy\left| {xy} \right.$$
ii) $$\,\,xy\left| {\left( {{x^ + }xy{y^ + }} \right)} \right.$$
iii) $${\,\,{x^ + }{y^ + }}$$
$$L = \left\{ {xn\,{y^n}\left| {n \ge 1} \right.} \right\} - $$ generates string where equal no. of $$x$$ and equal no. of $$y's.$$
$$E \to XBy\left| {xy\,abo} \right.$$ generators tips same.

The number of sub-strings (of all lengths inclusive) that can be formed from a character string of length $$n$$ is

The regular expression for the language recognized by the finite state automation of is _________.