Search results
Results from the WOW.Com Content Network
In computer science, Thompson's construction algorithm, also called the McNaughton–Yamada–Thompson algorithm, [1] is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). [2] This NFA can be used to match strings against the regular expression.
In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages .
The set of all strings accepted by an NFA is the language the NFA accepts. This language is a regular language. For every NFA a deterministic finite automaton (DFA) can be found that accepts the same language. Therefore, it is possible to convert an existing NFA into a DFA for the purpose of implementing a (perhaps) simpler machine.
Glushkov's algorithm can be used to transform it into an NFA, which furthermore is small by nature, as the number of its states equals the number of symbols of the regular expression, plus one. Subsequently, the NFA can be made deterministic by the powerset construction and then be minimized to get an optimal automaton corresponding to the ...
the DFA with a minimum number of states for a particular regular language (Minimization Problem) DFAs are equivalent in computing power to nondeterministic finite automata (NFAs). This is because, firstly any DFA is also an NFA, so an NFA can do what a DFA can do.
Regular languages are a category of languages (sometimes termed Chomsky Type 3) which can be matched by a state machine (more specifically, by a deterministic finite automaton or a nondeterministic finite automaton) constructed from a regular expression. In particular, a regular language can match constructs like "A follows B", "Either A or B ...
The NFA below has four states; state 1 is initial, and states 3 and 4 are accepting. Its alphabet consists of the two symbols 0 and 1, and it has ε-moves. The initial state of the DFA constructed from this NFA is the set of all NFA states that are reachable from state 1 by ε-moves; that is, it is the set {1,2,3}.
Converting this NFA to a DFA using the standard powerset construction (keeping only the reachable states of the converted DFA) leads to a DFA for the same reversed language. As Brzozowski (1963) observed, repeating this reversal and determinization a second time, again keeping only reachable states, produces the minimal DFA for the original ...