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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
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 ...
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 ...
Automata which can move back-and-forth on the input are called two-way finite automata. Acceptance condition. Acceptance of finite words: Same as described in the informal definition above. Acceptance of infinite words: an ω-automaton cannot have final states, as infinite words never terminate. Rather, acceptance of the word is decided by ...
In the theory of computation, a generalized nondeterministic finite automaton (GNFA), also known as an expression automaton or a generalized nondeterministic finite state machine, is a variation of a nondeterministic finite automaton (NFA) where each transition is labeled with any regular expression. The GNFA reads blocks of symbols from the ...
In automata theory and sequential logic, a state-transition table is a table showing what state (or states in the case of a nondeterministic finite automaton) a finite-state machine will move to, based on the current state and other inputs.
Formally, a deterministic finite automaton A may be defined by the tuple (Q, Σ, δ, q 0, F), where Q is the set of states of the automaton, Σ is the set of input symbols, δ is the transition function that takes a state q and an input symbol x to a new state δ(q,x), q 0 is the initial state of the automaton, and F is the set of accepting ...
A read-only Turing machine or two-way deterministic finite-state automaton (2DFA) is class of models of computability that behave like a standard Turing machine and can move in both directions across input, except cannot write to its input tape.