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The algorithm works recursively by splitting an expression into its constituent subexpressions, from which the NFA will be constructed using a set of rules. [3] More precisely, from a regular expression E , the obtained automaton A with the transition function Δ [ clarification needed ] respects the following properties:
Union (cf. picture); that is, if the language L 1 is accepted by some NFA A 1 and L 2 by some A 2, then an NFA A u can be constructed that accepts the language L 1 ∪L 2. Intersection; similarly, from A 1 and A 2 an NFA A i can be constructed that accepts L 1 ∩L 2. Concatenation; Negation; similarly, from A 1 an NFA A n can be constructed ...
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 computer science theory – particularly formal language theory – Glushkov's construction algorithm, invented by Victor Mikhailovich Glushkov, transforms a given regular expression into an equivalent nondeterministic finite automaton (NFA).
A GNFA must have only one transition between any two states, whereas a NFA or DFA both allow for numerous transitions between states. In a GNFA, a state has a single transition to every state in the machine, although often it is a convention to ignore the transitions that are labelled with the empty set when drawing generalized nondeterministic ...
In automata theory (a branch of theoretical computer science), NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states, transitions, or both. While efficient algorithms exist for DFA minimization, NFA minimization is PSPACE-complete. [1]
Reversing the transitions of a non-deterministic finite automaton (NFA) and switching initial and final states [note 1] produces an NFA for the reversal of the original language. Converting this NFA to a DFA using the standard powerset construction (keeping only the reachable states of the converted DFA) leads to a DFA M D R {\displaystyle M_{D ...
Chandra et al. [1] proved that converting an -state AFA to an equivalent DFA requires states in the worst case, though a DFA for the reverse language can be constructued with only states. Another construction by Fellah, Jürgensen and Yu.
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