MIN-MAX is an NFA-based algorithm for matching regular expressions composed of character classes with constraint repetitions (CCR). It is well-suited for parallel processing architectures like FPGAs. MIN-MAX uses (MIN, MAX) counters to dynamically track the lower and upper bounds of possible matching counts for each CCR engine, rather than actual matching counts. This counter-based design uses O(log n) memory bits to support constraint repetitions of n, rather than O(n) used in other solutions. MIN-MAX can resolve character class ambiguity and support overlapped matching when matching collisions are absent by using heuristic rules to assess collision absence. Testing on rule sets showed the majority see no collisions.

1. MIN-MAX A COUNTER-BASED ALGORITHM FOR REGULAR
EXPRESSION MATCHING
ABSTRACT:
We propose an NFA-based algorithm called MIN-MAX to support matching of regular
expressions (regexp) composed of Character Classes with Constraint Repetitions (CCR). MIN-
MAX is well suited for massive parallel processing architectures, such as FPGAs, yet it is
effective on any other computing platform. In MIN-MAX, each active CCR engine (to
implement one CCR term) evaluates input characters, updates (MIN, MAX) counters, and asserts
control signals, and all the CCR engines implemented in the FPGA run simultaneously. Unlike
traditional designs, (MIN, MAX) counters contain dynamically updated lower and upper bounds
of possible matching counts, instead of actual matching counts, so that feasible matching lengths
are compactly enclosed in the counter value.
The counter-based design can support constraint repetitions of n using O({rm log} n) memory
bits rather than that of O(n) in existing solutions. MIN-MAX can resolve character class
ambiguity between adjacent CCR terms and support overlapped matching when matching
collisions are absent. We developed a set of heuristic rules to assess the absence of collision for
CCR-based regexps, and tested them on Snort and SpamAssassin rule sets. The results show that
the vast majority of rules are immune from collisions, so that MIN-MAX can cost effectively
support overlapped matching. As a bonus, the new architecture also supports fast reconfiguration
via ordinary memory writes rather than resynthesis of the entire design, which is critical for time-
sensitive regexp deployment scenarios.
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