This preview shows pages 1–2. Sign up to view the full content.
Pumping Lemma
David Dill
Department of Computer Science
1
Outline
•
Push Down Automata introduction
•
Language of a PDA
•
Acceptance by final state vs. empty stack
•
Equivalence of CFGs and PDAs
•
Contextfree pumping lemma.
2
PDA Formalities
(
Q,
Σ
,
Γ
, δ, q
0
, Z
0
, F
)
Γ
is the
stack alphabet
.
Z
0
is the
start symbol
. PDA starts with
Z
0
on the stack and nothing else.
δ
:
Q
×
(Σ
∪
²
)
×
Γ
→
2
Q
×
Γ
*
(The value of
δ
must be a
finite
set, though.)
δ
bases possible next configuration on: the current state, the input (or
²
), and the
top symbol on the stack.
It gets a set of nondeterministic choices, each of which specifies the next state
and a string of new symbols to be pushed on the stack
Everything else is as in an eNFA
3
Acceptance by a PDA
An instantaneous description is a snapshot of the PDA:
Def
An
instantaneous description
of a PDA is
•
The current state.
•
The complete contents of the stack.
•
The input that has not yet been read.
So an ID has the type
Q
×
Σ
*
×
Γ
*
. E.g.,
(
q, w, α
)
, where
q
is the current
state,
w
is the unread input, and
α
is the stack (with the top symbol first).
The ID has everything necessary to predict the possible future IDs of the PDA.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Winter '08
 Motwani,R
 Computer Science

Click to edit the document details