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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.
In the theory of computation, a branch of theoretical computer science, a deterministic finite automaton (DFA)—also known as deterministic finite acceptor (DFA), deterministic finite-state machine (DFSM), or deterministic finite-state automaton (DFSA)—is a finite-state machine that accepts or rejects a given string of symbols, by running ...
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).
On the consumption of the last input symbol, if one of the current states is a final state, the machine accepts the string. A string of length n can be processed in time O(ns 2), [15] and space O(s). Create multiple copies. For each n way decision, the NFA creates up to n−1 copies of the machine. Each will enter a separate state.
It can only choose a new state, the result of following the transition. A pushdown automaton (PDA) differs from a finite state machine in two ways: It can use the top of the stack to decide which transition to take. It can manipulate the stack as part of performing a transition. A pushdown automaton reads a given input string from left to right.
State diagrams can be used to graphically represent finite-state machines (also called finite automata). This was introduced by Claude Shannon and Warren Weaver in their 1949 book The Mathematical Theory of Communication. Another source is Taylor Booth in his 1967 book Sequential Machines and Automata Theory.
A two-way deterministic finite automaton (2DFA) is an abstract machine, a generalized version of the deterministic finite automaton (DFA) which can revisit characters already processed. As in a DFA, there are a finite number of states with transitions between them based on the current character, but each transition is also labelled with a value ...
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 and only one transition to a next state. DFAs recognize the set of regular languages and no other languages. [1]: 52 A standard way to build a deterministic finite automaton from ...