Theory-of-Computation

Let M = ({q₀, q₁}, {0, 1}, {z₀, x}, δ, q₀, z₀, ∅) be a pushdown automaton where δ is given by

δ(q₀, 1, z₀) = {(q₀, xz₀)}
δ(q₀, ε, z₀) = {(q₀, ε)}
δ(q₀, 1, X) = {(q₀, XX)}
δ(q₁, 1, X) = {(q₁, ε)}
δ(q₀, 0, X) = {(q₁, X)}
δ(q₀, 0, z₀) = {(q₀, z₀)}

(a) What is the language accepted by this PDA by empty stack?

(b) Describe informally the working of the PDA.