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

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

(q, Y) ∈ δ(p, a, X).

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

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

Consider the following language.

L = { w ∈ {0, 1}* | w ends with the substring 011}

Which one of the following deterministic finite automata accepts L?

Let $$\left\langle M \right\rangle $$ denote an encoding of an automation M. Suppose that ∑ = {0, 1}. Which of the following languages is/are NOT recursive?

Given below are two statements I and II and two conclusions I and II :

Statement :

I. All bacteria are microorganisms.

II. All pathogens are microorganisms.

Conclusions :

I. Some pathogens are bacteria.

II. All pathogens are not bacteria

Based on the above statements and conclusions, which one of the following options is logically CORRECT?