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The instances of the DFA minimization problem that cause the worst-case behavior are the same as for Hopcroft's algorithm. The number of steps that the algorithm performs can be much smaller than n , so on average (for constant s ) its performance is O ( n log n ) or even O ( n log log n ) depending on the random distribution on automata chosen ...
Brzozowski's algorithm for DFA minimization uses the powerset construction, twice. It converts the input DFA into an NFA for the reverse language, by reversing all its arrows and exchanging the roles of initial and accepting states, converts the NFA back into a DFA using the powerset construction, and then repeats its process.
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.
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.
An example of an accepting state appears in Fig. 5: a deterministic finite automaton (DFA) that detects whether the binary input string contains an even number of 0s. S 1 (which is also the start state) indicates the state at which an even number of 0s has been input. S 1 is therefore an accepting state. This acceptor will finish in an accept ...
Nov. 30—Sen. Charles E. Schumer and a Western New York Representative are pushing for Canada to close a loophole in their immigration laws that's leading to long lines at northern border crossings.
An early application of partition refinement was in an algorithm by Hopcroft (1971) for DFA minimization. In this problem, one is given as input a deterministic finite automaton, and must find an equivalent automaton with as few states as possible. Hopcroft's algorithm maintains a partition of the states of the input automaton into subsets ...
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 of DFA states and simulation from this state continues.