Getting Started

1. Open the Simulation: Launch the DFA Minimization and Equivalence visualization in your web browser
2. Review the Interface: The simulation displays parallel DFA minimization with side-by-side comparison, interactive choice selection, and step-by-step minimization traces
3. Choose Your DFAs: Use the "Change DFAs" button to select different DFA pairs for comparison

Understanding the Interface

Dual-DFA Visualization

• Left Panel: "DFA A Minimization" - shows step-by-step partitioning process for the first DFA
• Right Panel: "DFA B Minimization" - displays parallel minimization steps for the second DFA
• Center Area: Interactive choice selection and current action display
• Visual Canvas: Side-by-side DFA diagrams showing states, transitions, and minimization progress

Main Controls

• Change DFAs: Switch between different DFA pairs to explore various equivalence scenarios
• Reset: Return to the beginning of the minimization process
• Previous Step: Go back to the previous partitioning step
• Show Hint: Get guidance on the correct choice for the current step
• Auto Step: Automatically apply the correct minimization step

Progress Tracking

• Score Display: Shows your accuracy in making correct minimization choices
• Current Turn: Indicates which DFA (A or B) you're currently working on
• Phase Display: Shows whether you're in the "Minimization" or "Equivalence" phase

Step-by-Step Procedure

Step 1: Select DFA Pair

1. Use Change DFAs to choose from available DFA examples
2. Observe the initial state diagrams for both DFA A and DFA B
3. Review the DFA descriptions to understand what languages they accept

Step 2: Remove Unreachable States

1. Identify Unreachable States: Look for states that cannot be reached from the start state
2. Choose Elimination Strategy: Select from 4 multiple-choice options for state removal
3. Visual Feedback: Watch as unreachable states are highlighted and removed from the diagram
4. Alternating Process: Take turns between DFA A and DFA B for each minimization step

Step 3: Initial Partitioning

1. Separate by Accepting Property: Partition states into accepting and non-accepting groups
2. Interactive Selection: Choose the correct partitioning strategy from the provided options
3. Partition Visualization: See how states are grouped and color-coded in the diagram

Step 4: Refine Partitions

1. Analyze Transition Behavior: Examine how states in each partition behave under input symbols
2. Identify Distinguishable States: Find states that transition to different partitions
3. Choose Refinement Steps: Select the appropriate partition refinement from multiple choices
4. Iterative Process: Continue until no further refinement is possible

Step 5: Compare Minimized DFAs

1. Final State Count: Compare the number of states in both minimized DFAs
2. Transition Structure: Examine the transition patterns in the final minimized forms
3. Equivalence Determination: Decide whether the minimized DFAs are structurally identical
4. Language Equivalence: Understand that identical minimized forms prove language equivalence