Associating ω-automata to path queries on Webs of Linked Data

The emergence of semantically enriched data sets along with the elegant way they are interconnected through the concept of Linked Data has drawn the attention of various scientific branches. The volume and the quality of information that lie inside the Linked Data, along with the capabilities they offer, make them ideal candidate to mine and extract valuable material, especially in field with great humanitarian importance, such as biology, medicine and social networks. As we show in this work, there are queries that cannot be expressed neither by standard SPARQL nor its expansion with regular path queries.These queries assume that the Web of Linked Data can be infinite and therefore classic queries expressed in terms of SPARQL need to be revisited. We propose a novel method associating a variant of automata that read infinite inputs, namely the ω-automata, to each query on this infinite structure. We call these queries ω-regular path queries due to the fact that they use ω  -regular expressions. These expressions are of the form a|(ab)ωa|(ab)ω. We present our approach through examples and figures, mainly inspired from systems related to biological functions and processes, providing indicative queries.