Automata and graph compression

We present a theoretical framework for the compression of automata, which are widely used representations in speech processing, natural language processing and many other tasks. As a corollary, our framework further covers graph compression. We introduce a probabilistic process of graph and automata generation that is similar to stationary ergodic processes and that covers real-world phenomena. We also introduce a universal compression scheme LZA for this probabilistic model and show that LZA significantly outperforms other compression techniques such as gzip and the UNIX compress command for several synthetic and real data sets.