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