# Theory of Computation: Question Set – 14

#### What is an NFA?

An NFA (Non-deterministic Finite Automaton) is a theoretical model of computation consisting of a finite set of states, an input alphabet, a transition function, an initial state, and one or more final states. It can be in more than one state at any given time and has the ability to make non-deterministic transitions.

#### What is the difference between NFA and DFA?

DFA (Deterministic Finite Automaton) can only be in one state at any given time, while an NFA can be in more than one state at a time. DFA always makes a transition for each input symbol, whereas an NFA can make multiple transitions or no transition for a given input symbol. Therefore, NFA can recognize a larger class of languages than DFA.

#### How is the transition function defined in an NFA?

The transition function in an NFA is a function that takes as input the current state and an input symbol, and returns a set of possible states that the NFA can transition to.

#### What is the language recognized by an NFA?

The language recognized by an NFA is the set of all strings that can be accepted by the NFA. A string is accepted by an NFA if there is a path of transitions from the initial state to a final state such that the input string is consumed by those transitions.

#### Can every NFA be converted into an equivalent DFA?

Yes, every NFA can be converted into an equivalent DFA using the subset construction algorithm. The resulting DFA will recognize the same language as the original NFA.

#### What is the time complexity of converting an NFA to an equivalent DFA?

The time complexity of converting an NFA to an equivalent DFA using the subset construction algorithm is O(2^{n}), where n is the number of states in the NFA. This is because the resulting DFA may have up to 2^{n} states in the worst case.

#### What is the difference between epsilon transitions and non-epsilon transitions in an NFA?

Epsilon transitions in an NFA are transitions that are made without consuming any input symbol. They are also called null transitions or lambda transitions. Non-epsilon transitions, on the other hand, are transitions that are made by consuming an input symbol.

#### What is the significance of epsilon closures in an NFA?

The epsilon closure of a state in an NFA is the set of all states that can be reached from that state through epsilon transitions alone. It is significant because it allows us to determine all the possible states that the NFA can be in at any given time, given its current set of states and input symbol. It is also used in the subset construction algorithm for converting an NFA to an equivalent DFA.

#### Can an NFA have multiple final states?

Yes, an NFA can have multiple final states. When an NFA has multiple final states, it means that it can accept a string if it ends in any one of those states.