SUffix trees meet REgular languages

Objective

The SURE project (SUffix trees meet REgular languages) is an interdisciplinary project at the intersection of several areas: Algorithms, Data Compression, Automata Theory and Bioinformatics. Its primary objective is to extend the suffix tree, the most important data structure for string processing, to labeled graphs and automata, and to use this new paradigm for studying regular languages. The suffix tree of a string supports a myriad of natural queries on strings, including multiple pattern matching variants. Suffix trees inspired a variety of related data structures for string algorithms, such as the suffix array, the Burrows-Wheeler transform and the FM-index. Today’s world demands the processing and analysis of increasingly complex, interrelated data. All these relationships can be captured by using (labeled) graphs. For example, the World Wide Web can be modeled as a graph, where elements are connected through hyperlinks. Graphs are also widely used to model social networks and to create databases. The SURE project will lead to a new data structure, the suffix tree of a graph, efficiently supporting all previous queries on graphs. This will be crucial in the emerging field of pangenomics, where graphs can store multiple genomes, overcoming the inherent bias of a single reference genome. Graphs provide a natural framework for analyzing regular languages in automata theory. Recent results indicate that several string-processing data structures suggest a new paradigm for analyzing regular languages. The SURE project will extend this paradigm through the suffix tree of a graph, proving that the same ideas can be applied to other formalisms (such as omega-regular languages). We will also show how to study the hierarchy of regular languages induced by these data structures through the lens of regular expressions and logic.