Pipelined Parallel Finite Automata Evaluation

Finite automata are key compute models in modern computational theory and important building blocks for digital logic used for regular expression and protocol parsing, filtering, and control. Finite automata evaluation would seem to be a sequential operation, since we need to complete the evaluation of one state to know the next state in which to evaluate the logic. Nonetheless, parallel theory provides strategies for parallel finite automata evaluation. We show how to exploit this parallel evaluation strategy in practice on today's high capacity FPGAs, including a novel formulation for spatially pipelined evaluation. For non-deterministic finite automata (NFA) with S states, we can evaluate N inputs in a single cycle with O(N * S
²
) BRAMs and O(N*S
³
) LUTs. This allows us, for example, to consume 64 inputs on a 16 state NFA in a single cycle on the Xilinx XZCU9EG-ffvb1156-2-i SoC FPGA, achieving 47 GB/s (377 Gb/s) single stream throughput for 8b inputs. For a 40 Gb/s network link, we can support 28 state NFAs.