# Finite State Machines ![[Pasted image 20241005231340.png]] # Deterministic vs Non-Deterministic FSM's Deterministic finite state machines (DFSMs) and non-deterministic finite state machines (NDFSMs) are two key types of FSMs with distinct characteristics. In a DFSM, each state transition is uniquely determined by the current state and input, allowing only one possible next state[1]. For example, a vending machine transitioning from 'Idle' to 'Selection' based on user input exemplifies a deterministic FSM[1]. Conversely, NDFSMs allow multiple transitions for a given input and current state, potentially resulting in multiple simultaneous states[1][2]. This non-deterministic behavior is illustrated by an elevator system where multiple paths can be taken to reach a desired floor[1]. While DFSMs are simpler and more commonly used, NDFSMs offer greater flexibility in modeling complex systems[3][4]. * DFSMs have exactly one transition for each input in every state[5]. * NDFSMs can have one, multiple, or no transitions for a given input and state[5]. * Any NDFSM can be converted to an equivalent (often more complex) DFSM using the powerset construction algorithm[5]. * DFSMs are easier to implement and analyze, while NDFSMs can sometimes provide more succinct representations of certain languages or systems[3][4]. # Finite State Machine Applications Finite state machines (FSMs) find widespread applications across various fields due to their ability to model complex systems with discrete states. In software development, FSMs are used to manage application states, simplify debugging, and ensure predictable behavior[1]. They are particularly valuable in game development for managing game states (e.g., menu, gameplay, pause) and character behaviors[1][2]. FSMs are also extensively utilized in hardware design, natural language processing, and robotics. In digital circuit design, FSMs are fundamental for creating sequential circuits like counters and controllers[3][4]. For natural language processing tasks, FSMs assist in text parsing, tokenization, and language understanding[5]. In robotics and autonomous systems, FSMs play a crucial role in controlling navigation, obstacle avoidance, and task execution based on sensor inputs and predefined rules[5]. Additionally, FSMs are employed in protocol analysis, speech recognition, and embedded systems for managing device states and responding to input events[6][1]. # State Transition Mechanisms State transition mechanisms in finite state machines (FSMs) can be broadly categorized into two types: owner-driven transitions and state-driven transitions[1]. In owner-driven transitions, the entity owning the FSM controls state changes, while in state-driven transitions, the states themselves initiate transitions. * Owner-driven transitions: The entity (e.g., a class) manages state changes, typically using a switch statement or lookup table to determine the next state based on current state and input[1]. * State-driven transitions: Each state object contains logic for determining its successor, often implemented using the State design pattern[1]. * Hybrid approaches: Some implementations combine both mechanisms for flexibility and maintainability[1]. * Output generation: Mealy machines produce output based on both current state and input, while Moore machines generate output solely based on the current state[2][3].