Path Logics for Querying Graphs: Combining Expressiveness and Efficiency

Abstract

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., subword, 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.

Foundations of Modern Query Languages for Graph Databases

“…A natural extension of ngps is to consider complex navigational graph patterns (cngps) by taking the closure of ngps under the relational operations of selection, projection, join, union, difference, and optional, as presented in Section 3. Some other variants and extensions of cngps allowing to compare different paths in a graph have also been considered in the past [Barceló et al 2012a;Barceló and Muñoz 2014;Figueira and Libkin 2015]. As we will see later in Section 4.4, cngps then form the core of languages such as SPARQL.…”

A Pattern Logic for Automata with Outputs

“…Related works In addition to the results already mentioned, we point out that the syntax of our logic is close to a logic, defined in [9] by Figueira and Libkin, to express path queries in graph databases (finite graphs with edges labelled by a symbol). In this work, there is no disjunction nor negation, and no distinction between input and output values.…”

“…The formal definition can be found e.g. in [9]. The counters allow us to compare the output length of paths, or to identify some output position of two paths with different labels (to test v ⊑ v ′ ).…”

On Computability of Data Word Functions Defined by Transducers

“…Overall, such pattern can be checked by a 2-counter Parikh automaton, whose emptiness is decidable in PTime [8] (under conditions that are satisfied here). Now, we move to the detailed proof.…”