Loading presentation...

Present Remotely

Send the link below via email or IM

Copy

Present to your audience

Start remote presentation

  • Invited audience members will follow you as you navigate and present
  • People invited to a presentation do not need a Prezi account
  • This link expires 10 minutes after you close the presentation
  • A maximum of 30 users can follow your presentation
  • Learn more about this feature in our knowledge base article

Do you really want to delete this prezi?

Neither you, nor the coeditors you shared it with will be able to recover it again.

DeleteCancel

Make your likes visible on Facebook?

Connect your Facebook account to Prezi and let your likes appear on your timeline.
You can change this under Settings & Account at any time.

No, thanks

CFG to PDA

No description
by

Zobaidul Karim

on 26 January 2014

Comments (0)

Please log in to add your comment.

Report abuse

Transcript of CFG to PDA

Context Free Grammars :
CFG to PDA
• Given: A context free grammar G
• Construct: A pushdown automata M
• Such that:
Language generated by G is the same as Language accepted by M.


Let’s formalize this:
Let G = (V, T, S, P) be a context
free grammar.
We define a pushdown automata
• M = (Q, Σ, Γ ,δ, q0, Z0 ,F)
Such that
• L(M) = L(G)

Step 6: CFG → PDA
Pushdown Automata :
• Basic idea
Use the stack of the PDA to simulate the
derivation of a string in the grammar.
• Push S (start variable of G) on the stack
• From this point on, there are two moves the PDA
can make:
1. If a variable A is on the top of the stack,pop
it and push the right-hand side of a production
A → β from G.
2.If a terminal, a is on the top of the stack,
pop it and match it with whatever symbol is being read from the tape.
Step 2: CFG → PDA
Step 5: CFG → PDA
Step 7: CFG → PDA
Step 4: CFG → PDA
Let’s formalize this :
Step 1: CFG → PDA
Step 8: CFG → PDA
• Let’s look at an example:
Remember the CFG for odd
length
palindromes:
• S → a | b
• S → a S a | b S b
Let’s convert this to a

PDA
.
Step 9: CFG → PDA

Example:
M = (Q, Σ, Γ ,δ, q0, Z0 ,F)
Q = { q0, q1, q2 }
Σ = { a, b }
Γ = { a, b, S, Z0 }
F = { q2 }

Step 10: CFG → PDA

Lots of moves
(see next slide)

Step 11: CFG → PDA
Let us convert the expression Grammar to PDA
The Grammar is:

I → a | b | Ia | Ib | I0 | I1
E → I | E*E | E+E | (E)
Step 12: CFG → PDA
• Let’s run M on abbba
(q0, abbba, Z) a (q1, abbba, SZ)
a (q1, abbba, aSaZ) // push
a (q1, bbba, SaZ) // match
a (q1, bbba, bSbaZ) // push
a (q1, bba, SbaZ) // match
a (q1, bba, bbaZ) // push
a (q1, ba, baZ) // match
a (q1, a, aZ) // match
a (q1, ε, Z) // match
a (q2, ε, Z ) // accept
The set of input symbols for PDA is {a, b, 0, 1, (,), +, *}. These eight symbols and the
symbols I and E from the stack alphabet. The transition function for the PDA is

a) δ(q, ε, I) = {(q, a), (q, b),
(q, Ia), (q, Ib), (q, I0), (q, I1)}
b) δ(q, ε, E) = {(q, I),(q, E+E),
(q,E*E),(q, (E))}
c) δ(q, a, a) = {(q, ε)}; δ(q, b, b) =
{( q, ε)}; δ(q, 0, 0) = {(q, ε)};
δ(q, 1, 1) = {(q, ε)}; δ(q,),() = {(q, ε)}; δ(q, ), )) = {(q, ε)}; δ(q, +, +) = {(q, ε)}; δ(q, *, *) = {(q, ε)}

Note that (a) and (b) come from rule (1), while the eight transition of (c) come from rule (2). Also, δ is empty except as defined by (a) through (c).
Try Another one
END
Full transcript