1. DETERMINISTIC CONTEXT FREE LANGUAGES
Ethakota Krishnamurthi Surendranath
Manoj Gujjari

2. What is a CFL(Context Free Language)?
Deterministic Context Free Language
Description
Properties
Importance

3. CONTEXT FREE LANGUAGES
A context-free language (CFL) is a language generated by some context-free grammar (CFG).
Different CF grammars can generate the same CF language, or conversely, a given CF language can be generated by different CF grammars.
The class of context-free languages generalizes the class of regular languages, i.e., every regular language is a context-free language.
The reverse of this is not true, i.e., every context-free language is not necessarily regular.

4. DCFL
Deterministic context-free languages are a proper subset of context-free languages.
Context free languages that can be accepted by Deterministic Push-Down Automata.
DCFLs are always unambiguous.
Many programming languages can be described by means of DCFLs.

5. DCFL Description Consider $: end of string marker Consider an example:
Let L = a*  {anbn : n > 0}.
When it begins reading a’s, M must push them onto the stack.
In case there are going to be b’s it runs out of input without seeing b’s, it needs a way to pop the a’s from the stack before it can accept.
The end-of-string marker allows the popping to happen, when all the input has been read.
Add $ to make it easier to build DPDAs, it does not add power (to allow building a PDA for L that was not context-free)
There exist CLFs that are not deterministic, e.g., L = {aibjck, i  j or j  k}.

6. A DETERMINISTIC PDA FOR L
L = a*  {anbn : n > 0}.

7. A NDPDA FOR L( No end-marker)
L = a*  {anbn : n > 0}.

8. Properties of DCFL DCFLS are not closed under union.
DCFLS are not closed under intersection.
DCFLS are closed under complement.

9. DCFLS are not closed under UNION
L1 = {aibjck, i, j, k  0 and i  j}. (a DCFL)
L2 = {aibjck, i, j, k  0 and j  k}. (a DCFL)
L = L1  L2.
= {aibjck, i, j, k  0 and (i  j) or (j  k)}.
L = L.
= {aibjck, i, j, k  0 and i = j = k} 
{w  {a, b, c}* : the letters are out of order}.
L = L  a*b*c*.
= {anbncn, n 0}.
L is not even CF, much less DCF.

10. DCFLS are not closed under Intersection
L1 = {aibjck, i, j, k  0 and i = j}.
L2 = {aibjck, i, j, k  0 and j = k}.
L = L1  L2 =
L1 and L2 are deterministic context-free:

11. CFL HIERARCHY

12. References Automata, Computability and Complexity, Elaine Rich.

13. QUESTIONS?