by this you will easily know the formal definitions.they will help to easily understand the basic definitions.

1. KANIMOZHI S
BE(CSE)

2. FINITE AUTOMATA
M={Q, ∑, δ,q0,F}
M-finite automata
Q-set of states
∑-inputs
δ-transition function(δ(Q* ∑)->Q)
q0-initial state
F-final state
this is a formal definition for finite automata.
 Deterministic finite automata(DFA) can also
be represented by same 5 tuples.

3. NON DETERMINISTIC FINITE AUTOMATA(NFA)
M={Q, ∑, δ,q0,F}
Q-set of states
∑-inputs
δ-transition function(δ(Q* ∑)->2^Q)
q0-initial state
F-final state
 Here the NFA it accepts same input as more
time.
 This is the major difference between DFA and
NFA
 The NFA with epsilon also denoted like this.
But there is transition function is
 δ’(Q* ∑*)->2^Q

4. CONTEXT FREE GRAMMAR
G={V,T,P,S}
V->non terminal
T->terminal
P->production
S->starting symbol
CGF it contains 4 tuples

5. P={Q, ∑, δ,q0,F,Π,Z0}
Q->set of states
∑->input symbol
δ->transition function
q0->initial state
F->final state
Π->finite stack symbols
Z0->starting symbol of stack
This is formal definition of PDA.

6. δ(q,a,x)=(p,γ)
q->current state
a->input symbol
x->top stack symbol
P->new state after reading a
γ
If γ=ε then stack will popped
If γ=x then stack not change
If γ=yz then x is replaced by z and y.