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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 ...
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.
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.
Optimizing an FSM means finding a machine with the minimum number of states that performs the same function. The fastest known algorithm doing this is the Hopcroft minimization algorithm. [19] [20] Other techniques include using an implication table, or the Moore reduction procedure. [21] Additionally, acyclic FSAs can be minimized in linear ...
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 ...
John Calipari recently likened playing in the SEC this season to sitting down at a poker table full of sharks. The Arkansas coach told reporters that he scanned the league standings from top to ...
The resulting program is faster than its table-driven counterpart [1] and much easier to debug and understand. Moreover, this approach often results in smaller lexers, [1] as re2c applies a number of optimizations such as DFA minimization and the construction of tunnel automaton. [9]