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The automaton reads the symbols of the input word and transitions between states until the word is read completely, if it is finite in length, at which point the automaton halts. A state at which the automaton halts is called the final state .
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.
According to the above definition, deterministic finite automata are always complete: they define from each state a transition for each input symbol. While this is the most common definition, some authors use the term deterministic finite automaton for a slightly different notion: an automaton that defines at most one transition for each state ...
For each input symbol, the NFA transitions to a new state until all input symbols have been consumed. In each step, the automaton nondeterministically "chooses" one of the applicable transitions. If there exists at least one "lucky run", i.e. some sequence of choices leading to an accepting state after completely consuming the input, it is ...
The word automaton is the latinization of the Ancient Greek automaton (αὐτόματον), which means "acting of one's own will".It was first used by Homer to describe an automatic door opening, [2] or automatic movement of wheeled tripods. [3]
In computer science, a deterministic automaton is a concept of automata theory where the outcome of a transition from one state to another is determined by the input. [ 1 ] : 41 A common deterministic automaton is a deterministic finite automaton (DFA) which is a finite state machine, where for each pair of state and input symbol there is one ...
Automata theory is the study of abstract machines (or more appropriately, abstract 'mathematical' machines or systems) and the computational problems that can be solved using these machines. These abstract machines are called automata. Automata comes from the Greek word (Αυτόματα) which means that something is doing something by itself.
A (nondeterministic) finite automaton is a quintuple A = Σ, S, s 0, δ, S f , where: Σ is the input alphabet (a finite, non-empty set of symbols), S is a finite, non-empty set of states, s 0 is the initial state, an element of S, δ is the state-transition relation: δ ⊆ S × Σ × S, and; S f is the set of final states, a (possibly empty ...