Nobody knows yet if $$P=NP$$. Consider the language $$L$$ defined as follows
$$L = \left\{ {\matrix{ {{{\left( {0 + 1} \right)}^ * }\,\,\,if\,\,P = NP} \cr {\,\,\,\,\,\,\,\phi \,\,\,\,Otherwise} \cr } } \right.$$

Which of the following statement is true?

If the strings of a language $$L$$ can be effectively enumerated in lexicographic (i.e., alphabetic$$(c)$$ order, which of the following statements is true?

Consider the following deterministic finite state automation $$M.$$

Let $$S$$ denote the set of seven bit binary strings in which the first, the fourth, and the last bits are $$1$$. The number of strings in $$S$$ that are accepted by $$M$$ is