PUSH-DOWN AUTOMATA

Pushdown Automata is a finite automata with extra memory called stack which helps Pushdown automata to recognize Context Free Languages.
A finite state machine just looks at the input signal and the current state: it has no stack to work with.
It chooses a new state, the result of following the transition.
A pushdown automaton (PDA) differs from a finite state machine in two ways:
1)It can use the top of the stack to decide which transition to take.
2)It can manipulate the stack as part of performing a transition.
A pushdown automaton reads a given input string from left to right.
In each step, it chooses a transition by indexing a table by input symbol, current state, and the symbol at the top of the stack.
A pushdown automaton can also manipulate the stack, as part of performing a transition.
The manipulation can be to push a particular symbol to the top of the stack, or to pop off the top of the stack.
The automaton can alternatively ignore the stack, and leave it as it is.

A Pushdown Automata (PDA) can be defined as:
P = ( Q, Σ, Γ, δ, q0, Z0, F)
Q : set of states
Σ : alphabet
Γ : stack alphabet
δ : transition function
q0 : start state
Z0 : start symbol
F : set of final states