Abstract
Derivatives of regular expressions were first introduced by Brzozowski in [1]. By recursively computing all derivatives of a regular expression, and associating a state with each unique derivative, a deterministic finite automaton can be constructed. Convergence of this process is guaranteed if uniqueness of regular expressions is recognized modulo associativity, commutativity, and idempotence of the union operator. Additionaly, through simplification based on the identities for regular expressions, the number of derivatives can be further reduced.
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References
Brzozowski, J.A.: Derivatives of Regular Expressions. Communications of the ACM 11, 481–494 (1964)
Hopkins, M.: Regular expression software. Posted to the comp.compilers newsgroup (1994), ftp://iecc.com/pub/file/regex.tar.gz
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© 2005 Springer-Verlag Berlin Heidelberg
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Frishert, M., Watson, B.W. (2005). Combining Regular Expressions with (Near-)Optimal Brzozowski Automata. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_34
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DOI: https://doi.org/10.1007/978-3-540-30500-2_34
Publisher Name: Springer, Berlin, Heidelberg
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