2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) (2015)
July 6, 2015 to July 10, 2015
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/LICS.2015.39
We study logics expressing properties of paths in graphs that are tailored to querying graph databases: a data model for new applications such as social networks, the Semantic Web, biological data, crime detection, and others. The basic construct of such logics, a regular path query, checks for paths whose labels belong to a regular language. These logics fail to capture two commonly needed features: counting properties, and the ability to compare paths. It is known that regular path-comparison relations (e.g., Prefix or equality) can be added without significant complexity overhead, however, adding common relations often demanded by applications (e.g., Sub word, subsequence, suffix) results in either undecidability or astronomical complexity. We propose, as a way around this problem, to use automata with counting functionalities, namely Parikh automata. They express many counting properties directly, and they approximate many relations of interest. We prove that with Parikh automata defining both languages and relations used in queries, we retain the low complexity of the standard path logics for graphs. In particular, this gives us efficient approximations to queries with prohibitively high complexity. We extend the best known decidability results by showing that even more expressive classes of relations are possible in query languages (sometimes with restriction on the shape of formulae). We also show that Parikh automata admit two convenient representations by analogs of regular expressions, making them usable in real-life querying.
Automata, Complexity theory, Database languages, Radiation detectors, Approximation methods, Query processing
Diego Figueira, Leonid Libkin, "Path Logics for Querying Graphs: Combining Expressiveness and Efficiency", 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), vol. 00, no. , pp. 329-340, 2015, doi:10.1109/LICS.2015.39