Push Down Automaton (PDA)
A Push Down Automaton (PDA) is a finite state machine with an additional stack that can store symbols. The stack allows the PDA to keep track of information beyond what can be stored in its finite set of states. The PDA can read input symbols, transition between states, and manipulate the stack based on the current state and input symbol.

Fixed Symbol in Stack
In a PDA, the stack can be used to store any symbols from the input alphabet. However, in this specific case, only one fixed symbol is allowed on the stack along with the input symbols. This means that the PDA can only push and pop the fixed symbol on the stack, while the input symbols are read and processed.

Counter Automaton
A counter automaton is a type of PDA that uses a stack to keep track of a counter value. The counter can be incremented or decremented by pushing or popping symbols on the stack. In this case, the fixed symbol on the stack can be used as a counter value.

Explanation
A counter automaton is the correct answer because it meets the requirements of the given scenario. The PDA can only have a fixed symbol on the stack, which can be used as a counter. The PDA can increment or decrement the counter value by pushing or popping the fixed symbol on the stack.

This type of PDA can be used to solve problems that require counting, such as verifying the balance of parentheses or checking the number of occurrences of a certain symbol in the input. The counter value can be used to keep track of the number of opening and closing parentheses, or the number of occurrences of a specific symbol, while processing the input.

By using a counter automaton, it is possible to solve problems that require counting using a PDA. The stack can be utilized as a counter by only allowing a fixed symbol on it, and the counter value can be incremented or decremented by pushing or popping the fixed symbol. This allows the PDA to keep track of additional information beyond its finite set of states.