[Verse 1] Seven-tuple definition, let me break it down for you Q for states, Sigma input, Gamma for the stack too Delta function guides the way, Q-zero starts the show Z-zero sits on bottom, F accepts what we know [Chorus] Push it down, push it down, PDA machine Stack memory, context-free, most powerful we've seen Push and pop, never stop, matching symbols clean From CFGs to PDAs, they're the same linguistic scene [Verse 2] Finite automaton with unlimited stack space Nondeterministic power gives it computational grace Delta maps from state and symbol, stack top in the mix To new state and string of symbols, that's how PDAs tick [Chorus] Push it down, push it down, PDA machine Stack memory, context-free, most powerful we've seen Push and pop, never stop, matching symbols clean From CFGs to PDAs, they're the same linguistic scene [Bridge] A-to-the-n, B-to-the-n, balanced parentheses too Palindromes need guessing games, nondeterministic through Deterministic PDAs are weaker than their kin Context-free equivalence is where the magic begins [Verse 3] Transition function takes three inputs, gives back a set State and symbol from the tape, stack symbol you get Pop the top and push new symbols, change state if you must Empty stack or final state means acceptance you can trust [Chorus] Push it down, push it down, PDA machine Stack memory, context-free, most powerful we've seen Push and pop, never stop, matching symbols clean From CFGs to PDAs, they're the same linguistic scene [Outro] Seven-tuple automaton, context-free and strong Push it down, the PDA song
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