Moore Machine with 6 Tuples

Moore Machine Components

• A Moore machine consists of 6 tuples: {Q, q0, Σ, Ο, δ, λ}
• Q is the set of states, in this case: {q0, q1, q2, q3, q4}
• q0 is the initial state

Input and Output Alphabets

• Σ (input alphabet) is the set of possible inputs: {a, b}
• Ο (output alphabet) is the set of possible outputs: {0, 1}

Output Mapping

• Output 0 is associated with input a
• Output 1 is associated with input b

Transition Rules (δ)

• Transition rules are defined as Q x Σ = Q, meaning every transition must follow the provided rules
• The transition table specifies the next state and output for each present state and input

Transition Table

• The transition table defines the behavior of the Moore machine for each possible input and state
• The table has the following structure:
  • Present State: the current state of the machine
  • Input a: the next state and output when input a is received
  • Input b: the next state and output when input b is received
  • Output: the output corresponding to the current state and input

Specific Transition Rules

• From q0: input a moves to q2 with output 1, input b moves to q1 with output 1
• From q1: input a moves to q3 with output 0, input b moves to q4 with output 0
• From q2: input a moves to q4 with output 1, input b moves to q1 with output 1
• From q3: input a moves to q4 with output 1, input b moves to q3 with output 1
• From q4: input a moves to q4 with output 0, input b moves to q4 with output 0