Gaëlle Fontaine

Why is it Hard to Obtain a Dichotomy for Consistent Query Answering

A database may for various reasons become inconsistent with respect to a given set of integrity constraints. To overcome the problem, a formal approach to querying such inconsistent databases has been proposed and since then, a lot of efforts have been spent to classify the complexity of consistent query answering under various classes of constraints. It is known that for the most common constraints and queries, the problem is in CONP and might be CONP-hard, yet several relevant tractable classes have been identified. Additionally, the results that emerged suggested that given a set of key constraints and a conjunctive query, the problem of consistent query answering is either in PTIME or is CONP-complete. However, despite all the work, as of today this dichotomy remains a conjecture. The main contribution of this paper is to explain why it appears so difficult to obtain a dichotomy result in the setting of consistent query answering. Namely, we prove that such a dichotomy w.r.t. common classes of constraints and queries, is harder to achieve than a dichotomy for the constraint satisfaction problem, which is a famous open problem since the 1990s.

On the Data Complexity of Consistent Query Answering

The framework of database repairs is a principled approach to managing inconsistency in databases. In particular, the consistent answers of a query on an inconsistent database provide sound semantics and the guarantee that the values obtained are those returned by the query on every repair of the given inconsistent database. In this paper, we carry out a systematic investigation of the data complexity of the consistent answers of conjunctive queries for set-based repairs and with respect to classes of constraints that, in recent years, have been extensively studied in the context of data exchange and data integration. Our results, which range from polynomial-time computability to undecidability, complement or improve on earlier work, and provide a fairly comprehensive picture of the data complexity of consistent query answering. We also address the problem of finding a “representative” or “useful” repair of an inconsistent database. To this effect, we introduce the notion of a universal repair, as well as relaxations of it, and then apply it to the investigation of the data complexity of consistent query answering.

Expressive Path Queries on Graphs with Data

Graph data models have recently become popular owing to their applications, e.g., in social networks, semantic web. Typical navigational query languages over graph databases — such as Conjunctive Regular Path Queries (CRPQs) — cannot express relevant properties of the interaction between the underlying data and the topology. Two languages have been recently proposed to overcome this problem: walk logic (WL) and regular expressions with memory (REM). In this paper, we begin by investigating fundamental properties of WL and REM, i.e., complexity of evaluation problems and expressive power. We first show that the data complexity of WL is nonelementary, which rules out its practicality. On the other hand, while REM has low data complexity, we point out that many natural data/topology properties of graphs expressible in WL cannot be expressed in REM. To this end, we propose register logic, an extension of REM, which we show to be able to express many natural graph properties expressible in WL, while at the same time preserving the elementariness of data complexity of REMs. It is also incomparable in expressive power against WL.

Expressive Path Queries on Graph with Data

Graph data models have recently become popular owing to their applications, e.g., in social networks and the semantic web. Typical navigational query languages over graph databases - such as Conjunctive Regular Path Queries (CRPQs) - cannot express relevant properties of the interaction between the underlying data and the topology. Two languages have been recently proposed to overcome this problem: walk logic (WL) and regular expressions with memory (REM). In this paper, we begin by investigating fundamental properties of WL and REM, i.e., complexity of evaluation problems and expressive power. We first show that the data complexity of WL is nonelementary, which rules out its practicality. On the other hand, while REM has low data complexity, we point out that many natural data/topology properties of graphs expressible in WL cannot be expressed in REM. To this end, we propose register logic, an extension of REM, which we show to be able to express many natural graph properties expressible in WL, while at the same time preserving the elementariness of data complexity of REMs. It is also incomparable to WL in terms of expressive power.

Why Is It Hard to Obtain a Dichotomy for Consistent Query Answering

A database may for various reasons become inconsistent with respect to a given set of integrity constraints. In the late 1990s, the formal approach of consistent query answering was proposed in order to query such databases. Since then, a lot of efforts have been spent to classify the complexity of consistent query answering under various classes of constraints. It is known that for the most common constraints and queries, the problem is in coNP and might be coNP-hard, yet several relevant tractable classes have been identified. Additionally, the results that emerged suggested that given a set of key constraints and a conjunctive query, the problem of consistent query answering is either in PTime or is coNP-complete. However, despite all the work, as of today this dichotomy remains a conjecture. The main contribution of this article is to explain why it appears so difficult to obtain a dichotomy result in the setting of consistent query answering. Namely, we prove that such a dichotomy with respect to common classes of constraints and queries is harder to achieve than a dichotomy for the constraint satisfaction problem, which is a famous open problem since the 1990s.

Cycle detection in computation tree logic

Abstract We introduce Cycle- CTL ⋆ , an extension of CTL ⋆ with cycle quantifications that are able to predicate over cycles. The introduced logic turns out to be very expressive. Indeed, we prove that it strictly extends CTL ⋆ and is orthogonal to μ Calculus . We also give an evidence of its usefulness by providing few examples involving non-regular properties. We extensively investigate both the model-checking and satisfiability problems for Cycle- CTL ⋆ and some of its variants/fragments.

On the data complexity of consistent query answering over graph databases

Areas in which graph databases are applied ‐ such as the semantic web, social networks and scientific databases ‐ are prone to inconsistency, mainly due to interoperability issues. This raises the need for understanding query answering over inconsistent graph databases in a framework that is simple yet general enough to accommodate many of its applications. We follow the well-known approach of consistent query answering (CQA), and study the data complexity of CQA over graph databases for regular path queries (RPQs) and regular path constraints (RPCs), which are frequently used. We concentrate on subset, superset and symmetric dierence repairs. Without further restrictions, CQA is undecidable for the semantics based on superset and symmetric dierence repairs, and P -complete for subset repairs. However, we provide several tractable restrictions on both RPCs and the structure of graph databases that lead to decidability, and even tractability of CQA. We also compare our results with those obtained for CQA in the context of relational databases. 1998 ACM Subject Classification H.2.3 Database Management - Query Languages

Cycle Detection in Computation Tree Logic.

Temporal logic is a very powerful formalism deeply investigated and used in formal system design and verification. Its application usually reduces to solving specific decision problems such as model checking and satisfiability. In these kind of problems, the solution often requires detecting some specific properties over cycles. For instance, this happens when using classic techniques based on automata, game-theory, SCC decomposition, and the like. Surprisingly, no temporal logics have been considered so far with the explicit ability of talking about cycles. In this paper we introduce Cycle-CTL*, an extension of the classical branching-time temporal logic CTL* along with cycle quantifications in order to predicate over cycles. This logic turns out to be very expressive. Indeed, we prove that it strictly extends CTL* and is orthogonal to mu-calculus. We also give an evidence of its usefulness by providing few examples involving non-regular properties. We investigate the model checking problem for Cycle-CTL* and show that it is PSPACE-Complete as for CTL*. We also study the satisfiability problem for the existential-cycle fragment of the logic and show that it is solvable in 2ExpTime. This result makes use of an automata-theoretic approach along with novel ad-hoc definitions of bisimulation and tree-like unwinding.

On the Data Complexity of Consistent Query Answering over Graph Databases

Areas in which graph databases are applied - such as the semantic web, social networks and scientific databases - are prone to inconsistency, mainly due to interoperability issues. This raises the need for understanding query answering over inconsistent graph databases in a framework that is simple yet general enough to accommodate many of its applications. We follow the well-known approach of consistent query answering (CQA), and study the data complexity of CQA over graph databases for regular path queries (RPQs) and regular path constraints (RPCs), which are frequently used. We concentrate on subset, superset and symmetric difference repairs. Without further restrictions, CQA is undecidable for the semantics based on superset and symmetric difference repairs, and Pi_2^P-complete for subset repairs. However, we provide several tractable restrictions on both RPCs and the structure of graph databases that lead to decidability, and even tractability of CQA. We also compare our results with those obtained for CQA in the context of relational databases.