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Pushdown Automata - Hampden-Sydney College

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Equivalence of PDAs and CFGs<br />

<strong>Pushdown</strong><br />

<strong>Automata</strong> -<br />

Equivalence<br />

to CFGs<br />

Robb T.<br />

Koether<br />

Homework<br />

Review<br />

Equivalence<br />

of PDAs and<br />

CFGs<br />

Proof ⇒<br />

Proof ⇐<br />

Long Example<br />

Short<br />

Example<br />

Assignment<br />

Proof (⇒).<br />

The transitions are<br />

δ(q 0 , ε, ε) = {(q 1 , $)}<br />

δ(q 1 , ε, ε) = {(q 2 , S)}<br />

δ(q 2 , ε, A) = {(q 2 , w)}, where A → w is a rule.<br />

δ(q 2 , a, a) = {(q 2 , ε)}, for all a ∈ Σ.<br />

δ(q 2 , ε, $) = {(q 3 , ε)}<br />

It is clear that L(M) = L(G).

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