Title: DPDA Deterministic PDA
1DPDADeterministic PDA
2Deterministic PDA DPDA
Allowed transitions
(deterministic choices)
3Allowed transitions
(deterministic choices)
4Not allowed
(non deterministic choices)
5DPDA example
6Definition
A language is deterministic context-free if
there exists some DPDA that accepts it
Example
The language
is deterministic context-free
7Example of Non-DPDA (PDA)
8Not allowed in DPDAs
9PDAs Have More Power thanDPDAs
10It holds that
Deterministic Context-Free Languages (DPDA)
Context-Free Languages PDAs
Since every DPDA is also a PDA
11We will actually show
Deterministic Context-Free Languages (DPDA)
Context-Free Languages (PDA)
12The language is
We will show
- is not deterministic context-free
13Language is context-free
14Theorem
The language
is not deterministic context-free
(there is no DPDA that accepts )
15Proof
Assume for contradiction that
is deterministic context free
Therefore
there is a DPDA that accepts
16DPDA with
accepts
accepts
17DPDA with
Such a path exists due to determinism
18Fact 1
The language is not
context-free
(we will prove this at a later class
using pumping lemma for context-free languages)
19Fact 2
The language is not
context-free
(we can prove this using pumping lemma for
context-free languages)
20We will construct a PDA that accepts
which is a contradiction!
21DPDA
Replace with
Modify
DPDA
22A PDA that accepts
Connect the final states of with the
final states of
23Since is accepted by a
PDA
it is context-free
Contradiction!
(since is not
context-free)
24Therefore
Is not deterministic context free
There is no DPDA that accepts it
End of Proof