Succinct Determinisation of Counting Automata via Sphere Construction

Abstract

We propose an efficient algorithm for determinising counting automata (CAs), i.e., finite automata extended with bounded counters. The algorithm avoids unfolding counters into control states, unlike the naïve approach, and thus produces much smaller deterministic automata. We also develop a simplified and faster version of the general algorithm for the sub-class of so-called monadic CAs (MCAs), i.e., CAs with counting loops on character classes, which are common in practice. Our main motivation is (besides applications in verification and decision procedures of logics) the application of deterministic (M)CAs in pattern matching regular expressions with counting, which are very common in e.g. network traffic processing and log analysis. We have evaluated our algorithm against practical benchmarks from these application domains and concluded that compared to the naïve approach, our algorithm is much less prone to explode, produces automata that can be several orders of magnitude smaller, and is overall faster.

Fast Matching of Regular Patterns with Synchronizing Counting (Technical Report)

“…In the context of regex matching, counting automata were used in several forms under several names (e.g. [29,23,24,25,28,31,1,32,33]). Besides [23] discussed above, other solutions to matching of counting regexes [25,24,26,27,28,29,30] handle small classes of regexes or do not allow matching linear in the text size and independent of counter bounds.…”

“…[29,23,24,25,28,31,1,32,33]). Besides [23] discussed above, other solutions to matching of counting regexes [25,24,26,27,28,29,30] handle small classes of regexes or do not allow matching linear in the text size and independent of counter bounds. The work [29] proposes a CA-to-CA determinization producing smaller automata than the explicit CA determinization for the limited class of monadic regexes, covered by letter-marked counting, and the size of their deterministic automata is still dependent on the counter bounds.…”

“…The problem of matching with bounded repetition has been addressed from the theoretical as well as from the practical perspective by a number of authors [25,24,26,27,28,29,30,23]. From these, the recent work [23] is the only one offering fast matching for a practically significant class of regexes.…”

Software-hardware codesign for efficient in-memory regular pattern matching

“…Several different automata models and automata-based techniques have been proposed to handle the matching of regexes with counting. DFAs and NFAs have been extended by [23] and [8] respectively by introducing counting operations and guards as an alternative to unfolding for large repetition bounds. An implementation of a class of counter automata, proposed in [59], is based on queues for representing sets of counter values.…”