Nondeterministic Finite Automata in Hardware - the Case of the Levenshtein Automaton

The Levenshtein Nondeterministic Finite state Automaton (NFA) recognizes input strings within a set edit distance of a configured pattern in linear time. This automaton can be pipelined to recognize all substrings of an input text in linear time with additional use of nondeterminism. In general, von Neumann hardware cannot directly execute NFAs without significant time or space overhead. A von Neumann simulation of the Levenshtein automaton incurs exponential run time overhead in the general case. A common technique to avoid the simulation overhead is to convert the pipelined NFA to a DFA, but at the expense of heavy pre-computation and high space overhead. In this paper, we introduce a novel technique for executing a pipelined Levenshtein NFA using Micron’s Automata Processor (AP), avoiding the run time and space overheads associated with CPU and GPU implementations. We show that run time remains linear with the input while the space requirement of the automaton becomes linear in the product of the configured pattern length and edit distance. These properties allow the AP to execute large instances of the Levenshtein NFA or many small instances in parallel thus making the automaton a viable building block for future approximate string applications on the AP.