Study Material

 1. Non-deterministic Finite Automata (NFA)   Unlike a DFA, an NFA allows a machine to explore multiple paths simultaneously.   Definition: For a given state and input symbol, an NFA can transition to zero, one, or multiple states . Acceptance: A string is accepted if at least one possible path leads to a final state. Flexibility: NFAs are generally easier to construct than DFAs because you don't need to define transitions for every possible input or worry about "dead states".   2. NFA with Epsilon Transitions ( ϵ epsilon 𝜖 -NFA)   An ϵ epsilon 𝜖 -NFA introduces the epsilon ( ϵ epsilon 𝜖 ) move , which allows the machine to change states without consuming any input symbol.   ϵ epsilon 𝜖 -Closure: This is a critical Day Three concept. It is the set of all states reachable from a specific state using only ϵ epsilon 𝜖 transitions (including the state itself). Use Case: ϵ epsilon 𝜖 -NFAs are highly useful for combining smaller machines (e.g., when ...

 1. The Formal Definition (The 5-Tuple)   A DFA is mathematically defined as a 5-tuple M = ( Q , Σ , δ , q 0 , F ) cap M equals open paren cap Q comma cap sigma comma delta comma q sub 0 comma cap F close paren 𝑀 = ( 𝑄 , Σ , 𝛿 , 𝑞 0 , 𝐹 ) :   Q cap Q 𝑄 : A finite set of states (e.g., { q 0 , q 1 , q 2 } the set q sub 0 comma q sub 1 comma q sub 2 end-set { 𝑞 0 , 𝑞 1 , 𝑞 2 } ). Σ cap sigma Σ : A finite set of symbols called the alphabet (e.g., { 0 , 1 } the set 0 comma 1 end-set { 0 , 1 } ). δ delta 𝛿 : The transition function , defined as δ ∶ Q × Σ → Q delta colon cap Q cross cap sigma right arrow cap Q 𝛿 ∶ 𝑄 × Σ → 𝑄 . This ensures that for every state and input, there is exactly one destination state. q 0 q sub 0 𝑞 0 : The start state ( q 0 ∈ Q q sub 0 is an element of cap Q 𝑞 0 ∈ 𝑄 ). F cap F 𝐹 : The set of accept states or final states ( F ⊆ Q cap F is a subset of or equal to cap Q 𝐹 ⊆ 𝑄 ).   2. Key Rules of DFA Design   Determini...