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A finite-state machine (FSM) or finite-state automaton (FSA, plural: automata), finite automaton, or simply a state machine, is a mathematical model of computation.It is an abstract machine that can be in exactly one of a finite number of states at any given time.
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).
A directed graph. 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
The figure illustrates a deterministic finite automaton using a state diagram. In this example automaton, there are three states: S 0, S 1, and S 2 (denoted graphically by circles). The automaton takes a finite sequence of 0s and 1s as input. For each state, there is a transition arrow leading out to a next state for both 0 and 1.
State complexity is an area of theoretical computer science dealing with the size of abstract automata, such as different kinds of finite automata.The classical result in the area is that simulating an -state nondeterministic finite automaton by a deterministic finite automaton requires exactly states in the worst case.
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.
A DFA for that language has at least 16 states. 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.
JFLAP allows one to create and simulate structures, such as programming a finite-state machine, and experiment with proofs, such as converting a nondeterministic finite automaton (NFA) to a deterministic finite automaton (DFA). JFLAP is developed and maintained at Duke University, with support from the National Science Foundation since 1993.