Automata and Graph Compression

TL;DR

This paper introduces a theoretical framework for automata and graph compression, proposing a universal scheme that outperforms traditional methods like gzip on various datasets.

Contribution

It develops a probabilistic model for automata and graph generation and introduces the LZA compression scheme, demonstrating its superior performance.

Findings

LZA outperforms gzip and UNIX compress on synthetic data

The framework effectively models real-world automata and graph data

LZA achieves significant compression improvements

Abstract

We present a theoretical framework for the compression of automata, which are widely used in speech processing and other natural language processing tasks. The framework extends to graph compression. Similar to stationary ergodic processes, we formulate a probabilistic process of graph and automata generation that captures real world phenomena and provide a universal compression scheme LZA for this probabilistic model. Further, we show that LZA significantly outperforms other compression techniques such as gzip and the UNIX compress command for several synthetic and real data sets.