State Machines

  1. Analysis and Optimization
    1. State Minimization
      1. Equivalent State Identification
        1. State Equivalence Criteria
          1. Equivalence Classes
          2. Partition Refinement
            1. Refinement Algorithms
              1. Convergence Criteria
              2. Hopcroft's Algorithm
                1. Algorithm Implementation
                  1. Complexity Analysis
                    1. Optimization Techniques
                    2. Myhill-Nerode Theorem
                      1. Theorem Applications
                        1. Minimization Proofs
                      2. Reachability Analysis
                        1. Unreachable State Detection
                          1. Graph Traversal Methods
                            1. Breadth-First Search
                              1. Depth-First Search
                              2. State Space Pruning
                              3. Property Verification
                                1. Liveness Properties
                                  1. Progress Guarantees
                                    1. Eventual Reachability
                                    2. Safety Properties
                                      1. Invariant Maintenance
                                        1. Error State Avoidance
                                        2. Deadlock Analysis
                                          1. Deadlock Detection
                                            1. Prevention Strategies
                                              1. Recovery Mechanisms
                                              2. Formal Verification Methods
                                                1. Model Checking
                                                  1. Temporal Logic
                                                    1. Verification Tools

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                                                8. Practical Applications

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                                                1. Introduction to State Machines