This document discusses the equivalence of deterministic finite automata (DFAs) and nondeterministic finite automata (NFAs). It defines DFAs and NFAs using 5-tuples and notes that while every DFA is an NFA, not every NFA is a DFA. However, the document states that there is always an equivalent DFA for every NFA using the subset construction method. Examples are provided of languages that could be recognized by a DFA or converted from an NFA to DFA using this method.

1. Equivalence of DFAs and NFAs
Submitted by – Samyak Jain (MCA/25014/2022) Submitted to – Madan Mohan Sir

2. DFA (Deterministic Finite Automata)
 It is the simplest model of computation.
 It has a very limited memory.
 DFA can be defined using five tuple (Q , ∑ , q0 ,F , δ)
Q = set of all states
∑ = inputs
q0 = start state/initial state
F = set of final states
δ = transition function Q × ∑ -> Q

3. NFA ( NonDeterministic Finite Automata )
 In NFA , given the current state there could be multiple next state.
 Next state may be chosen at random.
 NFA can be defined using five tuple (Q , ∑ , q0 ,F , δ)
Q = set of all states
∑ = inputs
q0 = start state/initial state
F = set of final states
δ = transition function Q × ∑ -> 2^Q

4. Equivalence of DFA and NFA
Two Automata are said to be equivalent if they
accept the same language.
Every DFA is an NFA , but not vice versa.
But there is an equivalent DFA for every NFA.

5. NFA to DFA conversion (Using subset
conversion method)
Ex -> L = { set of all string over (0,1) that starts with ‘0’}

6. Ex - > L = { set of all string over {0,1} that ends with ‘01’ }

7. Reference :-
https://youtu.be/--CSVsFIDng
https://neuraldump.net/2017/11/nfa-and-dfa-equivalence-theorem-proof-
and-example/

8. THANK YOU!!!