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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 ...
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 ...
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.
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 and only one transition to a next state.
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.
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 ...
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
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