HAL (Le Centre pour la Communication Scientifique Directe), Mar 28, 2023
GQL (Graph Query Language) is being developed as a new ISO standard for graph query languages to ... more GQL (Graph Query Language) is being developed as a new ISO standard for graph query languages to play the same role for graph databases as SQL plays for relational. In parallel, an extension of SQL for querying property graphs, SQL/PGQ, is added to the SQL standard; it shares the graph pattern matching functionality with GQL. Both standards (not yet published) are hard-to-understand specifications of hundreds of pages. The goal of this paper is to present a digest of the language that is easy for the research community to understand, and thus to initiate research on these future standards for querying graphs. The paper concentrates on pattern matching features shared by GQL and SQL/PGQ, as well as querying facilities of GQL.
Threshold queries are an important class of queries that only require computing or counting answe... more Threshold queries are an important class of queries that only require computing or counting answers up to a specified threshold value. To the best of our knowledge, threshold queries have been largely disregarded in the research literature, which is surprising considering how common they are in practice. We explore how such queries appear in practice and present a method that can be used to significantly improve the asymptotic bounds of their state-of-the-art evaluation algorithms. Our experimental evaluation of these methods shows order-of-magnitude performance improvements.
We investigate the problem of finite entailment of ontologymediated queries. We consider the expr... more We investigate the problem of finite entailment of ontologymediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCR-PQs), extending the well-known class of union of conjunctive queries, with regular expressions over roles. We look at ontologies formulated using the description logic ALC, and show a tight 2EXPTIME upper bound for entailment of UCR-PQs. At the core of our decision procedure, there is a novel automata-based technique introducing a stratification of interpretations induced by the deterministic finite automaton underlying the input UCRPQ.
For a given regular language of infinite trees, one can ask about the minimal number of prioritie... more For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a non-deterministic, alternating, or weak alternating parity automaton. These questions are known as, respectively, the non-deterministic, alternating, and weak Rabin-Mostowski index problems. Whether they can be answered effectively is a long-standing open problem, solved so far only for languages recognizable by deterministic automata (the alternating variant trivializes). We investigate a wider class of regular languages, recognizable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition. Game automata are known to recognize languages arbitrarily high in the alternating Rabin-Mostowski index hierarchy; that is, the alternating index problem does not trivialize any more. Our main contribution is that all three index problems are decidable for languages recognizable by game automata. Additionally, we show that it is decidable whether a given regular language can be recognized by a game automaton.
ACM Transactions on Database Systems, Jun 30, 2016
Containment of monadic datalog programs over trees is decidable. The situation is more complex wh... more Containment of monadic datalog programs over trees is decidable. The situation is more complex when tree nodes carry labels from an infinite alphabet that can be tested for equality. Then, it matters whether descendant relation is allowed or not: descendant relation can be eliminated easily from monadic programs only when label equalities are not used. With descendant, even containment of linear monadic programs in unions of conjunctive queries is undecidable and positive results are known only for bounded-depth trees. We show that without descendant containment of connected monadic programs is decidable over ranked trees, but over unranked trees it is decidable only for linear programs. With descendant it becomes decidable over unranked trees under restriction to downward programs: in each rule we only go down from the node in the head. This restriction is motivated by the formalism of regular tree pattern queries, recently proposed in the area of ActiveXML, which we show to be equivalent to linear downward programs.
The task of XML data exchange is to restructure a document conforming to a source schema under a ... more The task of XML data exchange is to restructure a document conforming to a source schema under a target schema according to certain mapping rules. The rules are typically expressed as source-to-target dependencies using various kinds of patterns, involving horizontal and vertical navigation, as well as data comparisons. The target schema imposes complex conditions on the structure of solutions, possibly inconsistent with the mapping rules. In consequence, for some source documents there may be no solutions. We investigate three problems: deciding if all documents of the source schema can be mapped to a document of the target schema (absolute consistency), deciding if a given document of the source schema can be mapped (solution existence), and constructing a solution for a given source document (solution building). We show that the complexity of absolute consistency is rather high in general, but within the polynomial hierarchy for bounded depth schemas. The combined complexity of solution existence and solution building behaves similarly, but the data complexity turns out to be very low. In addition to this we show that even for much more expressive mapping rules, based on MSO definable queries, absolute consistency is decidable and data complexity of solution existence is polynomial.
We provide a complete description of the Wadge hierarchy for deterministically recognisable sets ... more We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to another. This extends Wagner's results on the hierarchy of ω-regular languages of words to the case of trees.
We investigate graph transformations, defined using Datalog-like rules based on acyclic conjuncti... more We investigate graph transformations, defined using Datalog-like rules based on acyclic conjunctive two-way regular path queries (acyclic C2RPQs), and we study two fundamental static analysis problems: type checking and equivalence of transformations in the presence of graph schemas. Additionally, we investigate the problem of target schema elicitation, which aims to construct a schema that closely captures all outputs of a transformation over graphs conforming to the input schema. We show all these problems are in EXPTIME by reducing them to C2RPQ containment modulo schema; we also provide matching lower bounds. We use cycle reversing to reduce query containment to the problem of unrestricted (finite or infinite) satisfiability of C2RPQs modulo a theory expressed in a description logic. CCS CONCEPTS • Theory of computation → Logic and databases.
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
We investigate the problem of finite entailment of ontology-mediated queries. We consider the exp... more We investigate the problem of finite entailment of ontology-mediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCRPQs), extending the well-known class of unions of conjunctive queries, with regular expressions over roles. We look at ontologies formulated using the description logic ALC, and show a tight 2ExpTime upper bound for finite entailment of UCRPQs.
Threshold queries are an important class of queries that only require computing or counting answe... more Threshold queries are an important class of queries that only require computing or counting answers up to a specified threshold value. To the best of our knowledge, threshold queries have been largely disregarded in the research literature, which is surprising considering how common they are in practice. In this paper, we present a deep theoretical analysis of threshold query evaluation and show that thresholds can be used to significantly improve the asymptotic bounds of state-of-the-art query evaluation algorithms. We also empirically show that threshold queries are significant in practice. In surprising contrast to conventional wisdom, we found important scenarios in real-world data sets in which users are interested in computing the results of queries up to a certain threshold, independent of a ranking function that orders the query results by importance.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 7, 2017
Schema mappings specify how data organized under a source schema should be reorganized under a ta... more Schema mappings specify how data organized under a source schema should be reorganized under a target schema. For tree-structured data, the interplay between these specifications and the complex structural conditions imposed by the schemas, makes schema mappings a very rich formalism. Classical data management tasks, well-understood in the relational model, once again become challenging theoretical problems. Recent results on non-mixing integrity constraints help to push the decidability frontier further for three such problems: consistency of mappings, membership in the composition of mappings, and query answering.
We investigate the problem of finite entailment of ontologymediated queries. We consider the expr... more We investigate the problem of finite entailment of ontologymediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCR-PQs), extending the well-known class of union of conjunctive queries, with regular expressions over roles. We look at ontologies formulated using the description logic ALC, and show a tight 2EXPTIME upper bound for entailment of UCR-PQs. At the core of our decision procedure, there is a novel automata-based technique introducing a stratification of interpretations induced by the deterministic finite automaton underlying the input UCRPQ.
HAL (Le Centre pour la Communication Scientifique Directe), Mar 28, 2023
GQL (Graph Query Language) is being developed as a new ISO standard for graph query languages to ... more GQL (Graph Query Language) is being developed as a new ISO standard for graph query languages to play the same role for graph databases as SQL plays for relational. In parallel, an extension of SQL for querying property graphs, SQL/PGQ, is added to the SQL standard; it shares the graph pattern matching functionality with GQL. Both standards (not yet published) are hard-to-understand specifications of hundreds of pages. The goal of this paper is to present a digest of the language that is easy for the research community to understand, and thus to initiate research on these future standards for querying graphs. The paper concentrates on pattern matching features shared by GQL and SQL/PGQ, as well as querying facilities of GQL.
Threshold queries are an important class of queries that only require computing or counting answe... more Threshold queries are an important class of queries that only require computing or counting answers up to a specified threshold value. To the best of our knowledge, threshold queries have been largely disregarded in the research literature, which is surprising considering how common they are in practice. We explore how such queries appear in practice and present a method that can be used to significantly improve the asymptotic bounds of their state-of-the-art evaluation algorithms. Our experimental evaluation of these methods shows order-of-magnitude performance improvements.
We investigate the problem of finite entailment of ontologymediated queries. We consider the expr... more We investigate the problem of finite entailment of ontologymediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCR-PQs), extending the well-known class of union of conjunctive queries, with regular expressions over roles. We look at ontologies formulated using the description logic ALC, and show a tight 2EXPTIME upper bound for entailment of UCR-PQs. At the core of our decision procedure, there is a novel automata-based technique introducing a stratification of interpretations induced by the deterministic finite automaton underlying the input UCRPQ.
For a given regular language of infinite trees, one can ask about the minimal number of prioritie... more For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a non-deterministic, alternating, or weak alternating parity automaton. These questions are known as, respectively, the non-deterministic, alternating, and weak Rabin-Mostowski index problems. Whether they can be answered effectively is a long-standing open problem, solved so far only for languages recognizable by deterministic automata (the alternating variant trivializes). We investigate a wider class of regular languages, recognizable by so-called game automata, which can be seen as the closure of deterministic ones under complementation and composition. Game automata are known to recognize languages arbitrarily high in the alternating Rabin-Mostowski index hierarchy; that is, the alternating index problem does not trivialize any more. Our main contribution is that all three index problems are decidable for languages recognizable by game automata. Additionally, we show that it is decidable whether a given regular language can be recognized by a game automaton.
ACM Transactions on Database Systems, Jun 30, 2016
Containment of monadic datalog programs over trees is decidable. The situation is more complex wh... more Containment of monadic datalog programs over trees is decidable. The situation is more complex when tree nodes carry labels from an infinite alphabet that can be tested for equality. Then, it matters whether descendant relation is allowed or not: descendant relation can be eliminated easily from monadic programs only when label equalities are not used. With descendant, even containment of linear monadic programs in unions of conjunctive queries is undecidable and positive results are known only for bounded-depth trees. We show that without descendant containment of connected monadic programs is decidable over ranked trees, but over unranked trees it is decidable only for linear programs. With descendant it becomes decidable over unranked trees under restriction to downward programs: in each rule we only go down from the node in the head. This restriction is motivated by the formalism of regular tree pattern queries, recently proposed in the area of ActiveXML, which we show to be equivalent to linear downward programs.
The task of XML data exchange is to restructure a document conforming to a source schema under a ... more The task of XML data exchange is to restructure a document conforming to a source schema under a target schema according to certain mapping rules. The rules are typically expressed as source-to-target dependencies using various kinds of patterns, involving horizontal and vertical navigation, as well as data comparisons. The target schema imposes complex conditions on the structure of solutions, possibly inconsistent with the mapping rules. In consequence, for some source documents there may be no solutions. We investigate three problems: deciding if all documents of the source schema can be mapped to a document of the target schema (absolute consistency), deciding if a given document of the source schema can be mapped (solution existence), and constructing a solution for a given source document (solution building). We show that the complexity of absolute consistency is rather high in general, but within the polynomial hierarchy for bounded depth schemas. The combined complexity of solution existence and solution building behaves similarly, but the data complexity turns out to be very low. In addition to this we show that even for much more expressive mapping rules, based on MSO definable queries, absolute consistency is decidable and data complexity of solution existence is polynomial.
We provide a complete description of the Wadge hierarchy for deterministically recognisable sets ... more We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to another. This extends Wagner's results on the hierarchy of ω-regular languages of words to the case of trees.
We investigate graph transformations, defined using Datalog-like rules based on acyclic conjuncti... more We investigate graph transformations, defined using Datalog-like rules based on acyclic conjunctive two-way regular path queries (acyclic C2RPQs), and we study two fundamental static analysis problems: type checking and equivalence of transformations in the presence of graph schemas. Additionally, we investigate the problem of target schema elicitation, which aims to construct a schema that closely captures all outputs of a transformation over graphs conforming to the input schema. We show all these problems are in EXPTIME by reducing them to C2RPQ containment modulo schema; we also provide matching lower bounds. We use cycle reversing to reduce query containment to the problem of unrestricted (finite or infinite) satisfiability of C2RPQs modulo a theory expressed in a description logic. CCS CONCEPTS • Theory of computation → Logic and databases.
The use of general descriptive names, registered names, trademarks, etc. in this publication does... more The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
We investigate the problem of finite entailment of ontology-mediated queries. We consider the exp... more We investigate the problem of finite entailment of ontology-mediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCRPQs), extending the well-known class of unions of conjunctive queries, with regular expressions over roles. We look at ontologies formulated using the description logic ALC, and show a tight 2ExpTime upper bound for finite entailment of UCRPQs.
Threshold queries are an important class of queries that only require computing or counting answe... more Threshold queries are an important class of queries that only require computing or counting answers up to a specified threshold value. To the best of our knowledge, threshold queries have been largely disregarded in the research literature, which is surprising considering how common they are in practice. In this paper, we present a deep theoretical analysis of threshold query evaluation and show that thresholds can be used to significantly improve the asymptotic bounds of state-of-the-art query evaluation algorithms. We also empirically show that threshold queries are significant in practice. In surprising contrast to conventional wisdom, we found important scenarios in real-world data sets in which users are interested in computing the results of queries up to a certain threshold, independent of a ranking function that orders the query results by importance.
HAL (Le Centre pour la Communication Scientifique Directe), Jun 7, 2017
Schema mappings specify how data organized under a source schema should be reorganized under a ta... more Schema mappings specify how data organized under a source schema should be reorganized under a target schema. For tree-structured data, the interplay between these specifications and the complex structural conditions imposed by the schemas, makes schema mappings a very rich formalism. Classical data management tasks, well-understood in the relational model, once again become challenging theoretical problems. Recent results on non-mixing integrity constraints help to push the decidability frontier further for three such problems: consistency of mappings, membership in the composition of mappings, and query answering.
We investigate the problem of finite entailment of ontologymediated queries. We consider the expr... more We investigate the problem of finite entailment of ontologymediated queries. We consider the expressive query language, unions of conjunctive regular path queries (UCR-PQs), extending the well-known class of union of conjunctive queries, with regular expressions over roles. We look at ontologies formulated using the description logic ALC, and show a tight 2EXPTIME upper bound for entailment of UCR-PQs. At the core of our decision procedure, there is a novel automata-based technique introducing a stratification of interpretations induced by the deterministic finite automaton underlying the input UCRPQ.
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