Regular Expression Matching Can Be Simple And Fast

Speaking of regexp. Interesting analysis of approaches to regexp design. Rob Pike shows up again in this. Those Unix guys had something going back then.

This is a tale of two approaches to regular expression matching. One of them is in widespread use in the standard interpreters for many languages, including Perl. The other is used only in a few places, notably most implementations of awk and grep. The two approaches have wildly different performance characteristics...

Notice that Perl requires over sixty seconds to match a 29-character string. The other approach, labeled Thompson NFA for reasons that will be explained later, requires twenty microseconds to match the string. That's not a typo. The Perl graph plots time in seconds, while the Thompson NFA graph plots time in microseconds: the Thompson NFA implementation is a million times faster than Perl when running on a miniscule 29-character string. The trends shown in the graph continue: the Thompson NFA handles a 100-character string in under 200 microseconds, while Perl would require over 1015 years. (Perl is only the most conspicuous example of a large number of popular programs that use the same algorithm; the above graph could have been Python, or PHP, or Ruby, or many other languages. A more detailed graph later in this article presents data for other implementations.)

It may be hard to believe the graphs: perhaps you've used Perl, and it never seemed like regular expression matching was particularly slow. Most of the time, in fact, regular expression matching in Perl is fast enough...

Today, regular expressions have also become a shining example of how ignoring good theory leads to bad programs. The regular expression implementations used by today's popular tools are significantly slower than the ones used in many of those thirty-year-old Unix tools.

This article reviews the good theory: regular expressions, finite automata, and a regular expression search algorithm invented by Ken Thompson in the mid-1960s. It also puts the theory into practice, describing a simple implementation of Thompson's algorithm. That implementation, less than 400 lines of C, is the one that went head to head with Perl above. It outperforms the more complex real-world implementations used by Perl, Python, PCRE, and others. The article concludes with a discussion of how theory might yet be converted into practice in the real-world implementations...

While writing the text editor sam in the early 1980s, Rob Pike wrote a new regular expression implementation, which Dave Presotto extracted into a library that appeared in the Eighth Edition. Pike's implementation incorporated submatch tracking into an efficient NFA simulation but, like the rest of the Eighth Edition source, was not widely distributed. Pike himself did not realize that his technique was anything new. Henry Spencer reimplemented the Eighth Edition library interface from scratch, but using backtracking, and released his implementation into the public domain. It became very widely used, eventually serving as the basis for the slow regular expression implementations mentioned earlier: Perl, PCRE, Python, and so on. (In his defense, Spencer knew the routines could be slow, and he didn't know that a more efficient algorithm existed. He even warned in the documentation, “Many users have found the speed perfectly adequate, although replacing the insides of egrep with this code would be a mistake.”) Pike's regular expression implementation, extended to support Unicode, was made freely available with sam in late 1992, but the particularly efficient regular expression search algorithm went unnoticed. The code is now available in many forms: as part of sam, as Plan 9's regular expression library, or packaged separately for Unix. Ville Laurikari independently discovered Pike's algorithm in 1999, developing a theoretical foundation as well.

Finally, any discussion of regular expressions would be incomplete without mentioning Jeffrey Friedl's book Mastering Regular Expressions, perhaps the most popular reference among today's programmers. Friedl's book teaches programmers how best to use today's regular expression implementations, but not how best to implement them. What little text it devotes to implementation issues perpetuates the widespread belief that recursive backtracking is the only way to simulate an NFA. Friedl makes it clear that he neither understands nor respects the underlying theory.

Regular expression matching can be simple and fast, using finite automata-based techniques that have been known for decades. In contrast, Perl, PCRE, Python, Ruby, Java, and many other languages have regular expression implementations based on recursive backtracking that are simple but can be excruciatingly slow. With the exception of backreferences, the features provided by the slow backtracking implementations can be provided by the automata-based implementations at dramatically faster, more consistent speeds.

Companion articles, not yet written, will cover NFA-based submatch extraction and fast DFA implementations in more detail.

Just goes to show that various benchmarks are relative, and there's likely a good bit of low-hanging fruit in Erlang's implementation.