Deterministic vs. Non Deterministic Finite Automata in Automata Processing

Abstract

Linear-time pattern matching engines have seen promising results using Finite Automata (FA) as their computation model. Among different FA variants, deterministic (DFA) and non-deterministic (NFA) are the most commonly used computation models for FA-based pattern matching engines. Moreover, NFA is the prevalent model in pattern matching engines on spatial architectures. The reasons are: i) DFA size, as in #states, can be exponential compared to equivalent NFA, ii) DFA cannot exploit the massive parallelism available on spatial architectures. This paper performs an empirical study on the #state of minimized DFA and optimized NFA across a diverse set of real-world benchmarks and shows that if distinct DFAs are generated for distinct patterns, #states of minimized DFA are typically equal to their equivalent optimized NFA. However, NFA is more robust in maintaining the low #states for some benchmarks. Thus, the choice of NFA vs. DFA for spatial architecture is less important than the need to generate distinct DFAs for each pattern and support these distinct DFAs' parallel processing. Finally, this paper presents a throughput study for von Neumann's architecture-based (CPU) vs. spatial architecture-based (FPGA) automata processing engines. The study shows that, based on the workload, neither CPU-based automata processing engine nor FPGA-based automata processing engine is the clear winner. If #patterns matched per workload increases, the CPU-based automata processing engine's throughput decreases. On the other hand, the FPGA-based automata processing engine lacks the memory spilling option; hence, it fails to accommodate an entire automata if it does not fit into FPGA's logic fabric. In the best-case scenario, the CPU has a 4.5x speedup over the FPGA, while for some benchmarks, the FPGA has a 32,530x speedup over the CPU.