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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 ...
Also, given an NFA, using the powerset construction one can build a DFA that recognizes the same language as the NFA, although the DFA could have exponentially larger number of states than the NFA. [ 15 ] [ 16 ] However, even though NFAs are computationally equivalent to DFAs, the above-mentioned problems are not necessarily solved efficiently ...
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.
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 ...
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.
TNFA determinization is based on the canonical powerset construction algorithm that converts an NFA to a DFA. The algorithm simulates NFA on all possible strings. At each step of the simulation, the active set of NFA states forms a new DFA state.
Given a DFA, the problem of determining if it has a synchronizing word can be solved in polynomial time [2] using a theorem due to Ján Černý. A simple approach considers the power set of states of the DFA, and builds a directed graph where nodes belong to the power set, and a directed edge describes the action of the transition function.