pushdown automata (pda)

ProofWe show that for all q i ,q j ∈ Q,u,v ∈ Σ ∗ ,A ∈ Γ,X ∈ Γ ∗ ,(q i ,uv,AX) ∗ ⊢ (q j ,v,X) ⇔ (q i Aq j ) ∗ ⇒ u,which implies (q 0 ,w,z) ∗ ⊢ (q f ,λ,λ) ⇔ (q 0 zq f ) ∗ ⇒ w.Suppose |u| = n. Then there are n − 1 increments andn decrements of stack size. For each of theseincrement/decrement we have a corresponding rule.Stringing these rules together we have (q i Aq j ) ∗ ⇒ u.Pushdown Automata – p. 17