An important consequence of this implementation When a new state is computed, it is stored in a cache so That is, the DFA is constructed from the NFAĭuring a search. )" that backtracking is O ( 2 n ) O(2^n) O ( 2 n ) and the submachine implementationįor the people that don't like confrontation, there's a hybrid approach that also keeps the linear time at the cost of backreferences and lookarounds:ġ. (but is slow in Java, Perl, PHP, Python, Ruby. I haven't made the calculations of theīacktracking approach, but Russ Cox says in his post "Regular Expression Matching Can Be Simple And Fast In the case of NFA, it depends on the algorithm. In terms of time complexity, a DFA can compute a match in linear time. So in some cases a minimized DFA can have less states than a NFA. This is a PSPACE-complete problem (and maybe NP-hard? i'm confused). It's also important to highlight that there are DFA minimization algorithms (though the DFA above is already minimized) and there are not algorithms for Well in the post "Determinism costs! A NFA with exponentially bigger DFA" by Owen Stephens. If you are curious about this specific case, it's explained really I'm cherry picking a worst case scenario and most transformations aren't that bad. The worst case example can clearly be seen here: Powerset construction, the DFA can have up to 2 n 2^n 2 n states. If you transform a NFA with n n n states to a DFA with the But since you can't have duplicated transitions, it can ItĪll comes to the classic problem: Speed vs Memory ™.ĭFA are really fast because they don't have to make any decisions nor backtrack. But that doesn't mean the difference between both doesn't matter. For every language recognized by a NFA you can find a DFA that also recognizes it. So it's a NFA Practical differences between NFA and DFAĪfter all that theory you might be thinking: Who cares about the transitions a state has? Does it even matter? Do NFA have more recognizing power than DFAs?Īre equivalent. This is equivalent to q 0 q_0 q 0 having two a a a transitions. Let's forget for a while about regex and just talk of finite automata as defined in formal language theory. My view is incredibly biased towards the first google result my incredibly thorough research NFA and DFA - The theory Warning: If you want to create a serious DFA regex engine you should definitively investigate a lot more besides this post.
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