True

An NFA (Nondeterministic Finite Automaton) can indeed be modified to allow transitions without input alphabets, along with one or more transitions on input symbols. This modification is achieved by introducing the concept of ε-transitions (epsilon transitions) in the NFA.

1. NFA Transition on Input Symbols:
In a regular NFA, every transition is associated with an input symbol from the alphabet. When a symbol is read from the input, the NFA transitions to the next state based on the current state and the input symbol.

2. Introduction of ε-Transitions:
An ε-transition is a special kind of transition that does not require any input symbol to be read. Instead, it allows the NFA to transition from one state to another without consuming any input symbol. The ε-transition is denoted by the Greek letter ε (epsilon).

3. Purpose of ε-Transitions:
The introduction of ε-transitions in an NFA provides additional flexibility and expressiveness. It allows the NFA to make transitions without consuming an input symbol. This can be useful in various scenarios, such as:
- Allowing the NFA to move from one state to another without any input requirement.
- Enabling the NFA to make multiple transitions simultaneously.
- Facilitating the creation of non-deterministic paths in the automaton.

4. Representing ε-Transitions:
In the transition diagram of an NFA, ε-transitions are usually represented by arcs labeled with the symbol ε. These arcs connect the states of the NFA and indicate the possibility of making a transition without consuming an input symbol.

5. NFA Modification:
To modify an NFA to allow transitions without input alphabets, the NFA's transition function is extended to include ε-transitions. This modification does not change the basic structure or functionality of the NFA but enhances its capabilities.

By allowing transitions without input alphabets, an NFA becomes more powerful and can recognize a wider range of languages. It can handle situations where the automaton needs to make transitions based on its current state alone, without relying on input symbols.