Chapter 2: Context-Free Languages

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Chapter 2.2, Pushdown Automata

A pushdown automaton (PDA) is a finite automaton that also has access to a stack with infinite memory.


Pushdown Automaton 6-Tuple

A pushdown automaton is a 6-tuple (Q, Σ, Γ, δ, q0, F), where Q, Σ, Γ, and F are all finite sets, and

  1. Q is the set of states,
  2. Σ is the input alphabet,
  3. Γ is the stack alphabet,
  4. δ: Q × Σε × Γε → P(Q × Γε) is the transition function,
  5. q0 is the start state, and
  6. F ⊆ Q is the set of accept states.

Lecture Problem

Active Learning Problem


PDA M accepts input w (w1...wm where each wi ∈ Σε) if there is a sequence of states r0, ..., rm ∈ Q and strings s0, ..., sm ∈ Γ* such that

  1. r0 = q0 and s0 = ε
  2. (ri+1, b) ∈ δ(ri, wi+1, a) for i = 0, 1, ..., m-1 where si = at and si+1 = bt for some a, b ∈ Γε and t ∈ Γ*
  3. rm ∈ F

In-Class Notes

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