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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}.
In particular, every DFA is also an NFA. Sometimes the term NFA is used in a narrower sense, referring to an NFA that is not a DFA, but not in this article. Using the subset construction algorithm, each NFA can be translated to an equivalent DFA; i.e., a DFA recognizing the same formal language. [1] Like DFAs, NFAs only recognize regular languages.
The initial state of N(s) is the initial state of the whole NFA. The final state of N(s) becomes the initial state of N(t). The final state of N(t) is the final state of the whole NFA. The Kleene star expression s * is converted to An ε-transition connects initial and final state of the NFA with the sub-NFA N(s) in between.
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 ...
For example, a paper in 1999 described how JFLAP now allowed one to experiment with construction type proofs, such as converting an NFA to a DFA to a minimal state DFA, and as another example, converting NPDA to CFG and vice versa. [6] In 2002 JFLAP was converted to Swing. In 2005-2007 a study was run with fourteen institutions using JFLAP.
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.
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. If the new state is identical to an existing DFA state, it is discarded and replaced with the existing one, and the current branch of simulation terminates. Otherwise the new state is added to the growing set ...
A DFA or NFA can easily be converted into a GNFA and then the GNFA can be easily converted into a regular expression by repeatedly collapsing parts of it to single edges until S = {s, a}. Similarly, GNFAs can be reduced to NFAs by changing regular expression operators into new edges until each edge is labelled with a regular expression matching ...