Consider the $$NFA$$ $$M$$ shown below.

Let the language accepted by $$M$$ be $$L.$$ Let $${L_1}$$ be the language accepted by the $$NFA$$, $${M_1}$$ obtained by changing the accepting state of $$M$$ to a non accepting state and by changing the non accepting state of $$M$$ to accepting states. Which of the following statements is true?

The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the same set as

Consider the set $$\sum {^ * } $$ of all strings over the alphabet $$\,\sum { = \,\,\,\left\{ {0,\,\,\,1} \right\}.\sum {^ * } } $$ with the concatenation operator for strings

A single tape Turing Machine $$M$$ has two states $${q_0}$$ and $${q_1}$$, of which $${q_0}$$ is the starting state. The tape alphabet of $$M$$ is $$\left\{ {0,\,\,1,\,\,B} \right\}$$ and its input alphabet is $$\left\{ {0,\,\,1} \right\}$$. The symbol $$B$$ is the blank symbol used to indicate end of an input string. The transition function of $$M$$ is described in the following table.

The table is interpreted as illustrated below. The entry $$\left( {{q_1},1,\,R} \right)$$ in row $${{q_0}}$$ and column $$1$$ signifies that if $$M$$ is in state $${{q_0}}$$ and reads $$1$$ on the current tape square, then it writes $$1$$ on the same tape square, moves its tape head one position to the right and transitions to state $${{q_1}}$$.

Which of the following statements is true about $$M?$$