Theory of Computation Questions Answers GATE 2023

Theory of Computation GATE Question Answers with Explanation.

Q4 – Consider the pushdown automaton (PDA) P below, which runs on the input alphabet {a, b}, has stack alphabet {⊥, A}, and has three states {s, p, q}, with s being the start state. A transition from state u to state v, labelled c/X/γ, where c is an input symbol or ϵ, X is a stack symbol, and γ is a string of stack symbols, represents the fact that in state u, the PDA can read c from the input, with X on the top of its stack, pop X from the stack, push in the string γ on the stack, and

go to state v. In the initial configuration, the stack has only the symbol ⊥ in it. The PDA accepts by empty stack.

Which one of the following options correctly describes the language accepted by P? (GATE 2023)

1. {a^mbⁿ | 1 ≤ m and n < m}

2. { a^mbⁿ | 0 ≤ n ≤ m}

3. { a^mbⁿ | 0 ≤ m and 0 ≤ n}

4. { a^m | 0 ≤ m} ∪ { bⁿ | 0 ≤ n}