In the world of [[Lens]] in Category Theory, a Moore machine is a type of state machine that is used to model systems with inputs and outputs. It is named after [[Edward F. Moore]], who introduced the concept in the context of digital circuits. In [[Lens]], a Moore machine is defined as a pair consisting of a state space and an output function. The state space represents all possible states that the machine can be in, while the output function determines what output is produced based on the current state. Formally, a Moore machine consists of: 1. A set of states: This set represents all possible states that the machine can be in. Each state has a unique identifier. 2. An input alphabet: This is a set of symbols that represent possible inputs to the machine. 3. An output alphabet: This is a set of symbols that represent possible outputs from the machine. 4. A transition function: This function maps each state and input symbol to the next state. 5. An output function: This function maps each state to an output symbol. The behavior of a Moore machine can be described through its transitions between states and its corresponding outputs. When an input symbol is provided to the machine, it transitions from its current state to the next state based on its transition function. Simultaneously, it produces an output symbol based on its output function. ![[MooreMachine.excalidraw]] [[MooreMachine.excalidraw|Go to Excalidraw]] Moore machines are commonly used in various applications such as digital circuit design, control systems, and communication protocols. In [[Lens]] and [[Category Theory]], they provide a framework for modeling and reasoning about systems with inputs and outputs, allowing for analysis and composition of complex systems using category-theoretic concepts. # Other kinds of machines in Category Theory In Category Theory, there are several other types of machines that are studied and analyzed. Some of these include: 1. Mealy machines: [[Mealy machine|Mealy machines]] are a type of finite state machine that takes both input and output into consideration when transitioning between states. They are often used in digital circuit design and communication protocols. 2. Deterministic finite automata (DFAs): DFAs are a type of finite state machine where the next state is uniquely determined by the current state and input symbol. They are commonly used in areas such as pattern recognition, lexical analysis, and compiler design. 3. Nondeterministic finite automata (NFAs): NFAs are similar to DFAs, but they allow for multiple possible transitions from a given state with a given input symbol. They are primarily used in theoretical computer science and automata theory. 4. Pushdown automata: Pushdown automata extend the capabilities of finite state machines by adding a stack memory component. This allows them to recognize context-free languages and is commonly employed in parsing algorithms, such as those used in compilers. 5. Petri nets: Petri nets are graphical models that represent systems composed of interacting entities or processes. They are used to analyze concurrency, synchronization, and resource sharing in various domains, including distributed systems, biological systems, and manufacturing processes. These are just a few examples of the different types of machines studied within Category Theory. Each type has its own unique properties and applications within computer science and other fields of study. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Moore machine") or contains(subject, "State Machine") ```