List of top Theory of Computation Questions

Consider the following deterministic finite automaton (DFA) defined over the alphabet, \( \Sigma = \{a, b\} \). Identify which of the following language(s) is/are accepted by the given DFA.


 

Consider the following two languages over the alphabet \( \{a, b, c\} \), where \( m \) and \( n \) are natural numbers. \[ L_1 = \{ a^m b^{m+n} c^{m+n} \mid m, n \geq 1 \} \] \[ L_2 = \{ a^m b^n c^{m+n} \mid m, n \geq 1 \} \] Which ONE of the following statements is CORRECT?
Consider the following two languages over the alphabet \( \{a, b\} \): \[ L_1 = \{ \alpha \beta \alpha \mid \alpha \in \{a, b\}^+ { and } \beta \in \{a, b\}^+ \} \] \[ L_2 = \{ \alpha \beta \alpha \mid \alpha \in \{a\}^+ { and } \beta \in \{a, b\}^+ \} \] Which ONE of the following statements is CORRECT?
A regular language \(L\) is accepted by a non-deterministic finite automaton (NFA) with \(n\) states. Which of the following statement(s) is/are FALSE?
Consider the following context-free grammar \(G\), where \(S\), \(A\), and \(B\) are the variables (non-terminals), \(a\) and \(b\) are the terminal symbols, \(S\) is the start variable, and the rules of \(G\) are described as:
\[ S \to aaB \mid Abb \] \[ A \to a \mid AaA \] \[ B \to b \mid bB \] Which ONE of the languages \(L(G)\) is accepted by \(G\)?