Regular Expressions with Binding over Data Words for Querying Graph Databases

Abstract

Abstract. Data words assign to each position a letter from a finite alphabet and a data value from an infinite set. Introduced as an abstraction of paths in XML documents, they recently found applications in querying graph databases as well. Those are actively studied due to applications in such diverse areas as social networks, semantic web, and biological databases. Querying formalisms for graph databases are based on specifying paths conforming to some regular conditions, which led to a study of regular expressions for data words.Previously studied regular expressions for data words were either rather limited, or had the full expressiveness of register automata, at the expense of a quite unnatural and unintuitive binding mechanism for data values. Our goal is to introduce a natural extension of regular expressions with proper bindings for data values, similar to the notion of freeze quantifiers used in connection with temporal logics over data words, and to study both language-theoretic properties of the resulting class of languages of data words, and their applications in querying graph databases.

Regular Expressions for Querying Data Graphs

“…In particular, we show that the complexity of query evaluation for REWB is Pspace-complete (Theorem 4), the same complexity as register automata. This is rather surprising (at least to us) because REWB is shown to considerably weaker than register automata [14,13]. In fact, we also show that the minimal witnessing paths for REWB queries can be exponentially long (Proposition 3).…”

“…It was however proved that this comes at a price. In particular, REWBs were shown strictly weaker in terms of expressive power than register automata or expressions with memory [13,14].…”

“…A natural question then arises about expressions in which data are bound to variables within a well defined scope similar to the one in firstorder logic. These expressions, called regular expressions with binding (REWB) were already examined from a language theoretic point of view in [14,13].…”

“…Despite the "negative" results, we believe our results can be interesting and useful to the community to weed out some of the potentially unfruitful approaches. This paper is an extended version of [13], where space limitations prohibited us from presenting the proofs. Here we present the detailed proofs of the results presented in [13].…”

“…This paper is an extended version of [13], where space limitations prohibited us from presenting the proofs. Here we present the detailed proofs of the results presented in [13].…”