List of top Theory of Computation Questions

Suppose that \(L_1\) is a regular language and \(L_2\) is a context-free language. Which one of the following languages is NOT necessarily context-free?

Consider the following deterministic finite automaton (DFA). The number of strings of length 8 accepted by the above automaton is \(\underline{\hspace{2cm}}\). 

Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string $\epsilon$ is divisible by three.
For a string \(w\), we define \(w^R\) to be the reverse of \(w\). Which of the following languages is/are context-free?
Consider the following two statements about regular languages:
\(S_1:\) Every infinite regular language contains an undecidable language as a subset.
\(S_2:\) Every finite language is regular.
Which one of the following choices is correct?
Let \(L_1\) be a regular language and \(L_2\) be a context-free language. Which of the following languages is/are context-free?
Let \(L \subseteq \{0,1\}^*\) be an arbitrary regular language accepted by a minimal DFA with \(k\) states. Which one of the following languages must necessarily be accepted by a minimal DFA with \(k\) states?