A **Finite State Machine (FSM)** is a computational model used to represent and control the sequence of states in a system, especially in applications where an entity must react to a series of inputs or events. FSMs are widely used in various fields, including computer science, electrical engineering, linguistics, and artificial intelligence, to model behavior, processes, and workflows. Also see [[Finite State Diagram]]. ### Key Concepts of Finite State Machines 1. **States**: These are distinct configurations or modes that the machine or system can be in. For instance, a vending machine might have states like "Idle," "Selecting Item," "Payment," and "Dispensing Item." 2. **Transitions**: These represent the changes from one state to another, triggered by specific events or inputs. For example, inserting money might transition a vending machine from "Idle" to "Selecting Item." 3. **Inputs**: These are external actions or signals that influence the FSM's transitions between states, such as a button press, a command, or a user input. 4. **Initial State**: The state in which the machine begins operation. 5. **Final State(s)**: These are the end points of the FSM, often representing the completion of a task. Some FSMs do not have final states and are designed to continue indefinitely. ### Types of Finite State Machines 1. **Deterministic Finite Automata (DFA)**: In a DFA, each state has exactly one transition for each possible input. This means the machine’s behavior is completely predictable for any sequence of inputs. 2. **Nondeterministic Finite Automata (NFA)**: In an NFA, a state can have multiple possible transitions for the same input, or no transition at all. NFAs are useful for theoretical purposes and are equivalent in power to DFAs, though they may seem more complex. 3. **Mealy and Moore Machines**: These are specific types of FSMs where outputs are associated with transitions (Mealy) or with states (Moore). Mealy machines produce outputs based on the state and input, while Moore machines produce outputs based solely on the state. ### Applications of Finite State Machines FSMs are particularly useful for systems that require predictable behavior and sequential logic. They are often used in: - **Control Systems**: Traffic lights, elevators, and other devices that operate in distinct phases. - **Digital Circuit Design**: FSMs help design circuits for specific behavior in response to inputs, like in processors and digital logic circuits. - **Text Processing and Parsing**: Compilers, interpreters, and regular expressions use FSMs to recognize patterns and execute language syntax checks. - **Artificial Intelligence**: FSMs can represent simple decision-making processes in games, chatbots, and automated tasks. ### Advantages of FSMs - **Simplicity**: FSMs provide a clear and structured approach to handling sequences of events or inputs. - **Predictability**: Because each input leads to a well-defined state transition, FSMs are excellent for applications requiring reliable, repeatable behavior. - **Scalability**: FSMs can be combined to form more complex models, enabling the design of systems with nested or hierarchical states. ### Limitations of FSMs - **State Explosion**: For highly complex systems with many states and transitions, the FSM model can become difficult to manage and visualize. - **Memory Constraints**: Each state and transition consumes memory, so large FSMs can be challenging to implement in limited environments. - **Limited Context Awareness**: FSMs do not maintain historical context beyond the current state unless specifically designed to, which can limit their flexibility in certain applications. ### Example of a Finite State Machine Consider a simple **turnstile gate** FSM, often found in subway systems: - **States**: Locked, Unlocked. - **Transitions**: - Insert Coin → Transition from Locked to Unlocked. - Push Gate → Transition from Unlocked back to Locked. In this FSM, inserting a coin unlocks the turnstile, allowing a person to pass through. Once they push the gate and go through, the turnstile locks again, requiring another coin for the next entry. ### Conclusion Finite State Machines offer a powerful, flexible framework for modeling and understanding sequential behavior and can be applied across domains from digital circuits to user interface design. Although simple, FSMs are essential in building complex systems that require predictable, responsive, and logically organized operations. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Finite State") or contains(subject, "FSM") sort title, authors, modified ```