Succinct Determinisation of Counting Automata via Sphere Construction

We propose an efficient algorithm for determinising counting automata(CAs), i.e., finite automata extended with bounded counters. The algorithm avoidsunfolding counters into control states, unlike the nave approach, and thus producesmuch smaller deterministic automata. We also develop a simplified and fasterversion 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 inpractice. Our main motivation is (besides applications in verification and decisionprocedures of logics) the application of deterministic (M)CAs in pattern matchingregular expressions with counting, which are very common in e.g. network trafficprocessing and log analysis. We have evaluated our algorithm against practicalbenchmarks from these application domains and concluded that compared to thenave approach, our algorithm is much less prone to explode, produces automatathat can be several orders of magnitude smaller, and is overall faster.