# deterministic automaton

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## deterministic automaton

(theory)
A finite-state automaton in which the overall course of the computation is completely determined by the program, the starting state, and the initial inputs. The class of problems solvable by such automata is the class P (see polynomial-time algorithm).

## Deterministic Automaton

a mathematical model of a system whose states change discretely with time in such a way that every state of the system is completely defined by the previous state and the input signal. A deterministic automaton is formally described in the form of the function f(Si, aj) = ak, where si is the input signal and aj is the previous state. A typical example of a deterministic automation is a digital computer, in which the state of all registers and cells is determined by their previous state and by the input signals. Deterministic automatons are a natural form for describing the logical structure of discrete computing devices. Conversion to nondeterministic automatons is possible both by the introduction of the probabilities of a change of states and by the free selection of the next state.

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Hopcroft (1971) has given an algorithm that computes the minimal automaton of a given deterministic automaton.
Given a deterministic automaton A, Hopcroft's algorithm computes the coarsest congruence which saturates the set F of final states.
Cal designed an essentially deterministic automaton (Figure 9).
Henry decided not to complete this line, but turned to a direct approach, trying to design a fully deterministic automaton (Figure 15).
Next, Henry designed a basically deterministic automaton (Figure 16), but with meaningful nondeterminism in [q.
He designed a fully deterministic automaton (Figure 17), which is almost correct, except for one missing essential transition (a self loop with b in [q.
Yet, both of them preferred to replace it with a deterministic automaton.
The other two students explained their choice of model by saying that they thought it was impossible to construct a deterministic automaton for this language.
Instead, he designed a deterministic automaton, by combining the initial and final states and adding transitions to create some dependency between the automata.
It is shown that an elementary soliton graph defines a deterministic automaton iff it reduces to a graph not containing even-length cycles.
NSF02] use classical algorithms to (1) build a marked deterministic automaton recognizing a regular expression and (2) translate into generating function (Chomsky-Schiitzenberger algorithm [CS63]); this provides the bivariate generating function counting the matches.
U] be the ordinary trie representing the set U, seen as a finite deterministic automaton (Q, [delta], [epsilon], T) where the set of states is Q = Pref (u) (prefixes of words in u), the initial state is [epsilon], the set of final states is T = [A.

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