Lecture 18: Non-Deterministic Finite Automata (NFA)

#NFA #Non-DeterministicFiniteAutomata #FiniteAutomata #TOC #TheoryofComputation
Definition: A NFA is a 5-tuple M = (Q, Σ, δ, q0, F), where
1. Q is a finite set, whose elements are called states,
2. Σ is a finite set, called the alphabet ; the elements of Σ are called symbols,
3. δ : Q × Σ → Q is a function, called the transition function. It takes state in Q and input
symbol in Σ as a argument and returns a subset of Q as ouput.

Note: The difference between DFA and the NFA is in the type of transition function (δ). In
NFA, δ is a function that takes a state and input symbol as arguments and returns a set of
zero, one, or more states as output but in case of DFA exactly only one state is returned as
output.
4. q0 is an element of Q; it is called the start state,
5. F is a subset of Q; the elements of F are called accept states.

Extended Transition Function of NFA
The extended transition function of NFA, is a transition function that takes twoarguments as input; a state q ∈ Q & a string w and returns a set of states that the NFA is in, if it starts in q & processes the string w.