The language [Tex]L=\{a^n b^n \mid n \geq 1\}[/Tex] is:

(GATE 2004 | MCQ | 1-mark)

In a pushdown automaton P=(Q,Σ,Γ,δ,q0,F), a transition of the form,

where p,q∈Q, a∈σ∪{ϵ}, X,Y,∈Γ∪{ϵ}, represents

(q,Y) ∈ δ(p,a,X) 

Consider the following pushdown automaton over the input alphabet Σ={a,b} and stack alphabet Γ={#,A}.

The number of strings of length 100 accepted by the above pushdown automaton is ___________ .

According to the formal 7-tuple definition of a Pushdown Automaton [Tex]M=(Q,\Sigma,\Gamma,\delta,q_0,Z,F)[/Tex], the transition function $\delta$ determines the machine's next move based on exactly three input parameters. What are these three parameters?

Consider the NPDA 〈Q = {q0, q1, q2}, Σ = {0, 1}, Γ = {0, 1, ⊥}, δ, q0, ⊥, F = {q2}〉, where (as per usual convention) Q is the set of states, Σ is the input alphabet, Γ is stack alphabet, δ is the state transition function, q0 is the initial state, ⊥ is the initial stack symbol, and F is the set of accepting states, The state transition is as follows:
👁 Q60

Which one of the following sequences must follow the string 101100 so that the overall string is accepted by the automaton?

The language {a^m bⁿ C^m+n | m, n ≥ 1} is

Which is correct ?

Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton, and pda(y) means that y is a pushdown automaton. Let equivalent be another predicate such that equivalent (a, b) means a and b are equivalent. Which of the following first order logic statements represents the following:

Each finite state automaton has an equivalent pushdown automaton.

👁 q31

Consider the transition diagram of a PDA given below with input alphabet ∑ = {a, b}and stack alphabet Γ = {X, Z}. Z is the initial stack symbol. Let L denote the language accepted by the PDA.

Consider the following languages:
L1 = {aⁿb^mcⁿ : m, n >= 1}
L2 = {aⁿbⁿc²ⁿ : n >= 1}
Which one of the following is TRUE?

For Σ = {a, b}, let us consider the regular language

L = {x ∣ x = a2 + 3k or x = b10 + 12k, k ≥ 0} 

Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for L?