Push Down Automata Representation

Introduction:
A push down automata (PDA) is a type of automaton that extends the capabilities of a finite automaton by adding a stack to store information. It is mainly used to recognize context-free languages.

Representation:
A push down automata can be represented using the following methods:

a) Transition Graph:
A transition graph, also known as a state diagram, represents the states of the PDA as nodes and the transitions between states as directed edges. Each edge is labeled with the input symbol, the symbol popped from the stack, and the symbol pushed onto the stack (if any). The transition graph provides a visual representation of how the PDA processes input and manipulates the stack.

b) Transition Table:
A transition table is a tabular representation of the PDA's transitions. It consists of rows and columns, where each row represents a state and each column represents an input symbol. The cells of the table contain information about the actions to be taken when a particular input symbol is encountered in a specific state. The table includes the next state, the symbol to be popped from the stack, and the symbol (or symbols) to be pushed onto the stack.

c) ID:
ID stands for Identifier, and it does not represent a valid method for representing a push down automata. Therefore, option 'C' is incorrect.

Conclusion:
A push down automata can be represented using a transition graph or a transition table. Both methods provide a clear depiction of the PDA's states, transitions, and stack manipulations. These representations are essential for understanding the behavior and functionality of a PDA. Therefore, the correct answer is option 'D' - all of the mentioned.