Regular expressions & finite automata.

Mike Harrison <>
Wed, 15 Aug 90 14:42:31 GMT

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Regular expressions & finite automata. (Mike Harrison) (1990-08-15)
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Newsgroups: comp.compilers
From: Mike Harrison <>
Keywords: lex
Organization: Compilers Central
Date: Wed, 15 Aug 90 14:42:31 GMT

In response to tfd!kent@uunet.UU.NET (Kent Hauser), John wrote:

[Given the well-known equivalence between regular expressions and finite
state machines (albeit not a one-to-one equivalence) there are many programs
that compile regular expressions into FSMs and then run them.

In my copy of Aho & Ullman - 'The theory of parsing translation and
compiling', regular sets are shown to be equivalent to:
    - regular expressions,
    - right linear grammars,
    - finite automata.

Thus, I don't quite understand the "albeit not a one-to-one
equivalence" above.

Incidentally, this book is an excellent reference for a rigorous treatment of
many aspects of language theory.


Michael P. Harrison - Software Group - Inmos Ltd. UK.
UK :, US :
[There are many equivalent DFAs that a regular expression can translate to,
and vice versa. After all, any regular expression can be written in
infinitely many equivalent ways, e.g. a(b|c) vs. ab|ac, or to be really
pedantic, x vs. (x|x) vs. (x|x|x) ... -John]

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