Recovering Grammar Relationships for the Java Language Specification

Grammar convergence is a method that helps discovering relationships between different grammars of the same language or different language versions. The key element of the method is the operational, transformation-based representation of those relationships. Given input grammars for convergence, they are transformed until they are structurally equal. The transformations are composed from primitive operators; properties of these operators and the composed chains provide quantitative and qualitative insight into the relationships between the grammars at hand. We describe a refined method for grammar convergence, and we use it in a major study, where we recover the relationships between all the grammars that occur in the different versions of the Java Language Specification (JLS). The relationships are represented as grammar transformation chains that capture all accidental or intended differences between the JLS grammars. This method is mechanized and driven by nominal and structural differences between pairs of grammars that are subject to asymmetric, binary convergence steps. We present the underlying operator suite for grammar transformation in detail, and we illustrate the suite with many examples of transformations on the JLS grammars. We also describe the extraction effort, which was needed to make the JLS grammars amenable to automated processing. We include substantial metadata about the convergence process for the JLS so that the effort becomes reproducible and transparent

The Vadalog System: Datalog-based Reasoning for Knowledge Graphs

Over the past years, there has been a resurgence of Datalog-based systems in the database community as well as in industry. In this context, it has been recognized that to handle the complex knowl\-edge-based scenarios encountered today, such as reasoning over large knowledge graphs, Datalog has to be extended with features such as existential quantification. Yet, Datalog-based reasoning in the presence of existential quantification is in general undecidable. Many efforts have been made to define decidable fragments. Warded Datalog+/- is a very promising one, as it captures PTIME complexity while allowing ontological reasoning. Yet so far, no implementation of Warded Datalog+/- was available. In this paper we present the Vadalog system, a Datalog-based system for performing complex logic reasoning tasks, such as those required in advanced knowledge graphs. The Vadalog system is Oxford's contribution to the VADA research programme, a joint effort of the universities of Oxford, Manchester and Edinburgh and around 20 industrial partners. As the main contribution of this paper, we illustrate the first implementation of Warded Datalog+/-, a high-performance Datalog+/- system utilizing an aggressive termination control strategy. We also provide a comprehensive experimental evaluation.Comment: Extended version of VLDB paper <https://doi.org/10.14778/3213880.3213888

The computability path ordering

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by lifting a precedence on function symbols. A first version, core CPO, is essentially obtained from the higher-order recursive path ordering (HORPO) by eliminating type checks from some recursive calls and by incorporating the treatment of bound variables as in the com-putability closure. The well-foundedness proof shows that core CPO captures the essence of computability arguments \'a la Tait and Girard, therefore explaining its name. We further show that no further type check can be eliminated from its recursive calls without loosing well-foundedness, but for one for which we found no counterexample yet. Two extensions of core CPO are then introduced which allow one to consider: the first, higher-order inductive types; the second, a precedence in which some function symbols are smaller than application and abstraction

The Complexity of Boolean Conjunctive Queries with Intersection Joins

Intersection joins over interval data are relevant in spatial and temporal data settings. A set of intervals join if their intersection is non-empty. In case of point intervals, the intersection join becomes the standard equality join. We establish the complexity of Boolean conjunctive queries with intersection joins by a many-one equivalence to disjunctions of Boolean conjunctive queries with equality joins. The complexity of any query with intersection joins is that of the hardest query with equality joins in the disjunction exhibited by our equivalence. This is captured by a new width measure called the IJ-width. We also introduce a new syntactic notion of acyclicity called iota-acyclicity to characterise the class of Boolean queries with intersection joins that admit linear time computation modulo a poly-logarithmic factor in the data size. Iota-acyclicity is for intersection joins what alpha-acyclicity is for equality joins. It strictly sits between gamma-acyclicity and Berge-acyclicity. The intersection join queries that are not iota-acyclic are at least as hard as the Boolean triangle query with equality joins, which is widely considered not computable in linear time

The Complexity of Reverse Engineering Problems for Conjunctive Queries

Reverse engineering problems for conjunctive queries (CQs), such as query by example (QBE) or definability, take a set of user examples and convert them into an explanatory CQ. Despite their importance, the complexity of these problems is prohibitively high (coNEXPTIME-complete). We isolate their two main sources of complexity and propose relaxations of them that reduce the complexity while having meaningful theoretical interpretations. The first relaxation is based on the idea of using existential pebble games for approximating homomorphism tests. We show that this characterizes QBE/definability for CQs up to treewidth k, while reducing the complexity to EXPTIME. As a side result, we obtain that the complexity of the QBE/definability problems for CQs of treewidth k is EXPTIME-complete for each k > 1. The second relaxation is based on the idea of "desynchronizing" direct products, which characterizes QBE/definability for unions of CQs and reduces the complexity to coNP. The combination of these two relaxations yields tractability for QBE and characterizes it in terms of unions of CQs of treewidth at most k. We also study the complexity of these problems for conjunctive regular path queries over graph databases, showing them to be no more difficult than for CQs