Partial derivatives of regular expressions and finite automaton constructions
Theoretical Computer Science
Derivatives of Regular Expressions
Journal of the ACM (JACM)
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Translating Regular Expressions into Small epsilon-Free Nondeterministic Finite Automata
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
Journal of Computer and System Sciences
Ambiguity in Graphs and Expressions
IEEE Transactions on Computers
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We examine several methods to obtain nondeterministic finite automata without Ɛ-transitions (NFA) from regular expressions. The focus is on the size (number of transitions) of the resulting automata, and on the time complexity of the transformation. We show how recent developments [9,6] have improved the size of the resulting automaton from O(n2) to O(n(log n)2), and even O(n log n) for bounded alphabet size (where n is the size of the regular expression). A lower bound [11] shows this to be close to optimal, and also one of those constructions can be computed in optimal time [8].