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A state S of the DFA is an accepting state if and only if at least one member of S is an accepting state of the NFA. [2] [3] In the simplest version of the powerset construction, the set of all states of the DFA is the powerset of Q, the set of all possible subsets of Q. However, many states of the resulting DFA may be useless as they may be ...
To decide whether two given regular expressions describe the same language, each can be converted into an equivalent minimal deterministic finite automaton via Thompson's construction, powerset construction, and DFA minimization. If, and only if, the resulting automata agree up to renaming of states, the regular expressions' languages agree.
The DFA can be constructed using the powerset construction. This result shows that NFAs, despite their additional flexibility, are unable to recognize languages that cannot be recognized by some DFA. It is also important in practice for converting easier-to-construct NFAs into more efficiently executable DFAs.
An example that can be used to demonstrate the powerset construction reducing NFAs to equivalent DFAs. The corresponding DFA is Image:DFA-powerset-construction-example.svg. Created by Derrick Coetzee in Adobe Illustrator based on the same source as en:Image:NFA-powerset-construction-example.png, which this replaces. Date
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 ...
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 ...
Let be the set of words over the alphabet {a,b} whose nth last letter is an .The figures show a DFA and a UFA accepting this language for n=2.. Deterministic automaton (DFA) for the language L for n=2 Unambiguous finite automaton (UFA) for the language L for n=2
An example that can be used to demonstrate the powerset construction reducing NFAs to equivalent DFAs. The corresponding NFA is Image:NFA-powerset-construction-example.svg. Created by Derrick Coetzee in Adobe Illustrator based on the same source as en:Image:DFA-powerset-construction-example.png, which this replaces. Date