Sublinear Matching With Finite Automata Using Reverse Suffix Scanning

TL;DR

This paper introduces algorithms to accelerate DFA computation by reverse scanning and offsetting automata, enabling significant input skipping and faster matching, adaptable to memory and time constraints.

Contribution

It presents offsetting finite automata (OFA) and algorithms for their construction and matching, allowing more input skipping than previous methods.

Findings

Over 80% input skipping in examples

Faster matching with OFA compared to previous algorithms

Adaptability to memory and time constraints

Abstract

We give algorithms to accelerate the computation of deterministic finite automata (DFA) by calculating the state of a DFA n positions ahead utilizing a reverse scan of the next n characters. Often this requires scanning fewer than n characters resulting in a fraction of the input being skipped and a commensurate increase in processing speed. The skipped fraction is > 80% in several of our examples. We introduce offsetting finite automata (OFA) to encode the accelerated computation. OFA generalize DFA by adding an integer offset to the current input index at each state transition. We give algorithms for constructing an OFA that accepts the same language as a DFA while possibly skipping input, and for matching with an OFA. Compared to previous algorithms that attempt to skip some of the input, the new matching algorithm can skip more often and can skip farther. In the worst case the new matching algorithm scans the same number of characters as a simple forward scan, whereas previous approaches often scan more, so the new algorithm can be used as a reliable replacement for the simple forward scan. Additionally, the new algorithm adapts to available memory and time constraints.