theory of automata

1. PUSHDOWN AUTOMATA
INTRODUCTION AND EXPLAINATION;

2. Context free grammar
 Context free grammar is the root of PDA.
 It is a generating device or it is the root of whole domain.
 It is generate CFL and the language that is generated by CFG is accepted by
PUSHDOWN AUTOMATA.
 Here we not concerned with context free grammar or PDA we just focus of CFL.
 PDA consist on two parts.
1. Deterministic PDA
2. Non deterministic PDA

3. CONT..
In case of finite automata;
The deterministic is not different with non deterministic, the DFA is already a subset
of NFA.
NFA can be translate into DFA; but here the phenomenon is different.
The power of NDPDA is greater then power of DPDA.
We cannot translate it because NDPDA has greater power.
NDPDA>DPDA

4. CONT…
 Context free language is defined as;
The language that we make PDA is called CFL.
Block diagram of PDA

5. Cont.. PDA
The power of NDPDA can accept all context free language but;
The power of DPDA cannot accept all context free language,, it accept some
languages, that language further divide into parts
 CFL
 DCFL(that accepts only deterministic pushdown automata).

6. Tuples of PUSHDOWN AUTOMATA
 A PDA can be formally described as a 7-tuple (Q, Σ, S, δ, q0, I, F):
 Q is the finite number of states
 Σ is input alphabet
 S is stack symbols
 δ is the transition function: Q × (Σ∪{ε}) × S × Q × S*
 q0 is the initial state (q0 ∈ Q)
 I is the initial stack top symbol (I ∈ S)
 F is a set of accepting states (F ∈ Q)

7. Point to be noted in PDA
 First it is the combination of FINITE AUTOMATA+ STACK.
 And why we use stack data structure in PDA whenever we have many type of data
structures?
ANSWER:-
Here we apply data structure to resolve memory; in other data structure the phenomenon
that is used, where we want to insert and where we want to delete an element; moreover
in other type of data structures we have a limited number of elements that we insert and
we check there UNDERFLOW & OVERFLOW.
In stack we push single element and when pop it, if the special symbol if we see it means
the stack is empty we don’t pop any more or not check the underflow.

8. Transition diagram of DPDA and NDPDA
respectively.

9. How to read PUSHDOWN AUTOMATA
There are three basic functionality to read push down automata.
 Push
 Pop
 Skip

10. Cont.. Push,

11. Cont.. Pop

12. Cont.. Skip

13. Example of PDA

14. Cont.. E.g.

15. THANK YOU!
NADIA
ROLL NO 22
BSCS 4TH SMESTER MORNING