This document discusses pushdown automata (PDA) and how they can be used to accept context-free languages. It defines a PDA as a 7-tuple that includes a finite set of states, input symbols, stack symbols, initial state, initial stack symbol, set of final states, and a transition function. A context-free grammar is also defined as a 4-tuple that includes variables, terminals, production rules, and a start symbol. The document then shows how to construct a PDA that is equivalent to a given context-free grammar by defining transition rules based on the grammar productions. An example of converting a grammar to a PDA using this construction method is also provided.

1. PUSH DOWN AUTOMATA

2. WHY PDA ?
 DFAs accept regular languages.
 We want to design machines similar to
DFAs that will accept context-free
languages and is regular.
 A finite automation cannot accept
string of the form (a^n,b^n) as it has to
remember the no. of a’s and so
requires infinite no. of states.

3. POWERS OF PDA
 This difficulty is avoided by adding a auxiliary
memory in form of stack.
 It has a read only input tape and input alphabet.
 Final state control
 Set of final states
 Initial state (as in FA)
 Read write push down store.

4. PDA MODEL

5. FORMAL DEFINATION
 Finite nonempty set of states Q.
 Finite non empty set of input symbols denoted
by
 Finite non empty set of pushdown store
 Initial state q0.
 Initial symbol of push down store Z0.
 Set of final state
 a transition function .



A PDA IS A 7 TUPLE ,NAMELY
 ),0,0,,,,( FZqQ 

6. FORMAL DEFINATION OF CFG
A context-free grammar G is a 4-tuple
(V, , R, S), where:
 V is a finite set; each element v  V is called a non-
terminal character or a variable.
  is a finite set of terminals, disjoint from , which
make up the actual content of the sentence.
 R is a finite relation from V to (V U )* .
 S, the start symbol, used to represent the whole
sentence (or program). It must be an element of V.

7. FORMAL CONTRUCTION
Let G = (V, T,R, S) be a CFG. The PDA P = ({q}, T,
V ∪ T, δ, q, S)
where the δ is defined as follows:
 For each variable A,
R1: δ(q, ǫ,A) = {(q, β) | A → β is a production of
R}
 For each terminal a
R2: δ(q, a, a) = {(q, ǫ)}
* Ǫ DENOTES NULL

8. PROJECT
CONTRUCT PDA EQUIVALENT TO FOLLOWING
GRAMMAR WITH PRODUCTIONS.
S -> a AA
S -> a S
A -> b S
A -> a
Convert to PDA using LL.
Show simulations

9. Step 1: Select GRAMMAR

11. STEP 2:Write the productions
STEP 3 : Covert ->PDA ( LL)

12. OUTPUT :

13. Construct CFG TO PDA
We define PDA A as
is defined by following rules:
),,,},,,,{},,{},({  SqbaASbaqA 

)},{(),,(:4
)},{(),,(:3
)},{(),,(:2
)},(),,(),,{(),,(:1




qbbqR
qaaqR
aqAqR
bSqaSqaAAqSqR





14. TEST FOR STRING ‘aabaaa’
),,(*
),,(
),,(
),,(
),,(
),,(
),,(
),,(
),,(
),,(
),,(











q
aaaaq
AAaaq
aAAaaaq
Saaaq
bSbaaaq
Sbaaaq
aSabaaaq
Sabaaaq
aSaabaaaq
Saabaaaq

15. THANK YOU