From Regular Expressions to DFA's Using Compressed NFA's

We show how to turn a regular expression R of length r into an O(s) space representation of McNaughton and Yamada's NFA, where s is the number of occurrences of alphabet symbols in R, and s+1 is the number of NFA states. The standard adjacency list representation of McNaughton and Yamada's NFA takes up s + s2 space in the worst case. The adjacency list representation of the NFA produced by Thompson takes up between 2r and 6r space, where r can be arbitrarily larger than s. Given any set V of NFA states, our representation can be used to compute the set U of states one transition away from the states in V in optimal time O(¦V¦+¦U¦). McNaughton and Yamada's NFA requires Θ(¦V¦ × ¦U¦) time in the worst case. Using Thompson's NFA, the equivalent calculation requires Θ(r) time in the worst case.

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