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An automaton with a finite number of states is called a finite automaton (FA) or finite-state machine (FSM). The figure on the right illustrates a finite-state machine, which is a well-known type of automaton. This automaton consists of states (represented in the figure by circles) and transitions (represented by arrows).
Finite-state machines are a class of automata studied in automata theory and the theory of computation. In computer science, finite-state machines are widely used in modeling of application behavior ( control theory ), design of hardware digital systems , software engineering , compilers , network protocols , and computational linguistics .
The set of states of automaton A, denoted states(A), need not be finite. This is a significant generalization of the usual notion of finite automata, as it enables modeling systems with unbounded data structures like counters and unbounded length queues. The set of start states (also known as initial states) is a non-empty subset of states.
In automata theory, a timed automaton is a finite automaton extended with a finite set of real-valued clocks. During a run of a timed automaton, clock values increase all with the same speed. Along the transitions of the automaton, clock values can be compared to integers.
A classic form of state diagram for a finite automaton (FA) is a directed graph with the following elements (Q, Σ, Z, δ, q 0, F): [2] [3] Vertices Q: a finite set of states, normally represented by circles and labeled with unique designator symbols or words written inside them; Input symbols Σ: a finite collection of input symbols or designators
A cellular automaton consists of a regular grid of cells, each in one of a finite number of states, such as on and off (in contrast to a coupled map lattice). The grid can be in any finite number of dimensions. For each cell, a set of cells called its neighborhood is defined relative to the specified cell.
In Automata theory, clocks are regarded as timed automatons, a type of finite automaton. Automaton clocks being finite essentially means that automaton clocks have a certain number of states in which they can exist. [71] The exact number is the number of combinations possible on a clock with the hour, minute, and second hand: 43,200.
In automata theory, a finite-state machine is called a deterministic finite automaton (DFA), if each of its transitions is uniquely determined by its source state and input symbol, and; reading an input symbol is required for each state transition.