Non-deterministic Pushdown Automata, Finite Automata with External Storage

Nondeterministic pushdown automat (NPDA):

Definition NPDA: M= (Q, A, B, f, q0, F) or M= (Q, A, B, f, q0) in the version ‘accept by empty stack’

Q, A, B, q0, F similar as above, however the transition function is different: f:  Q x Aε x Bε ->  2QxB*

Notice: The non-deterministic PDAs are much powerful acceptors than the deterministic PDAs.

Example: The 2-state NPDA M accepts (through empty stack) even palindromes, L0 = {w wreverse | w ∈ {0, 1}*}.

p, 0, ε -> p, 0 ;   p, 1, ε -> p, 1  (p supposes M is still reading the first half of input string)

p, ε, ε -> q, ε  (non-deterministic guess of midpoint)

q, 0, 0 -> q, ε,   q, 1, 1 -> q, ε  (q supposes M is reading the second half of the input string).

A) ∀ wwreverse, w ∈ {0, 1}*, ∃ a sequence of transitions driven by the wwreverse that outcomes in an empty stack.

B) ∀ z ≠ wwreverse, no sequence of the transitions driven by z outcomes in an empty stack.

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