Pushdown Automata - Hampden-Sydney College

Group 1 Rules
Pushdown
Automata -
Equivalence
to CFGs
Robb T.
Koether
Homework
Review
Equivalence
of PDAs and
CFGs
Proof ⇒
Proof ⇐
Long Example
Short
Example
Assignment
Example (Convert a PDA to a CFG)
That gives 54 rules.
We can eliminate the ones containing variables of the
form A xp for x ≠ p and A ux for x ≠ u.
That eliminates 12 rules, leaving 42.
A ps → A px A xs for all x ∈ Q, x ≠ u
A pq → A px A xq for all x ∈ Q, x ≠ u
A pu → A px A xu for all x ∈ Q
A qs → A qx A xs for all x ∈ Q, x ≠ p, u
A qq → A qx A xq for all x ∈ Q, x ≠ p, u
A qu → A qx A xu for all x ∈ Q, x ≠ p
A ss → A sx A xs for all x ∈ Q, x ≠ p, u
A sq → A sx A xq for all x ∈ Q, x ≠ p, u
A su → A sx A xu for all x ∈ Q, x ≠ p