DFA (Deterministic Finite Automaton)

A DFA is defined as a 5-tuple M = (Q, Σ, δ, q₀, F) where:

• Q = Finite set of states
• Σ = Finite set of input symbols (alphabet)
• δ = Transition function, δ: Q × Σ → Q
• q₀ = Initial/start state, q₀ ∈ Q
• F = Set of final/accepting states, F ⊆ Q

Moore Machine

A Moore machine is defined as a 6-tuple M = (Q, q₀, Σ, Λ, δ, λ) where:

• Q = Finite set of states
• q₀ = Initial state, q₀ ∈ Q
• Σ = Input alphabet (finite set of input symbols)
• Λ = Output alphabet (finite set of output symbols)
• δ = Transition function, δ: Q × Σ → Q
• λ = Output function, λ: Q → Λ (output depends only on state)

Mealy Machine

A Mealy machine is defined as a 6-tuple M = (S, S₀, Σ, Λ, T, G) where:

• S (or Q) = Finite set of states
• S₀ = Start/initial state, S₀ ∈ S
• Σ = Input alphabet (finite set of input symbols)