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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.
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 ...
In a non-deterministic automaton, an input can lead to one, more than one, or no transition for a given state. The powerset construction algorithm can transform any nondeterministic automaton into a (usually more complex) deterministic automaton with identical functionality. A finite-state machine with only one state is called a "combinatorial ...
Deterministic: For a given current state and an input symbol, if an automaton can only jump to one and only one state then it is a deterministic automaton. Nondeterministic : An automaton that, after reading an input symbol, may jump into any of a number of states, as licensed by its transition relation.
[2] Prior to that it was unknown whether it is possible to perform submatch extraction in one pass on a deterministic finite-state automaton, so this paper was an important advancement. Laurikari described TDFA construction and gave a proof that the determinization process terminates, however the algorithm did not handle disambiguation correctly.
With the further aid of nondeterminism the machine can parse any context-free language. With two infinite stacks the machine is Turing equivalent and can parse any recursive formal language . If the machine is allowed to have multiple tape heads, it can parse any language in L or NL , according to whether nondeterminism is allowed.
The state of a deterministic finite automaton = (,,,,) is unreachable if no string in exists for which = (,).In this definition, is the set of states, is the set of input symbols, is the transition function (mapping a state and an input symbol to a set of states), is its extension to strings (also known as extended transition function), is the initial state, and is the set of accepting (also ...
In computer science, a deterministic acyclic finite state automaton (DAFSA), [1] is a data structure that represents a set of strings, and allows for a query operation that tests whether a given string belongs to the set in time proportional to its length. Algorithms exist to construct and maintain such automata, [1] while keeping them minimal.