First-Order Query Evaluation with Cardinality Conditions

We study an extension of first-order logic that allows to express cardinality conditions in a similar way as SQL's COUNT operator. The corresponding logic FOC(P) was introduced by Kuske and Schweikardt (LICS'17), who showed that query evaluation for this logic is fixed-parameter tractable on classes of structures (or databases) of bounded degree. In the present paper, we first show that the fixed-parameter tractability of FOC(P) cannot even be generalised to very simple classes of structures of unbounded degree such as unranked trees or strings with a linear order relation. Then we identify a fragment FOC1(P) of FOC(P) which is still sufficiently strong to express standard applications of SQL's COUNT operator. Our main result shows that query evaluation for FOC1(P) is fixed-parameter tractable with almost linear running time on nowhere dense classes of structures. As a corollary, we also obtain a fixed-parameter tractable algorithm for counting the number of tuples satisfying a query over nowhere dense classes of structures

Answering Conjunctive Queries under Updates

We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear$^\ast$ delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis. $^\ast)$ By sublinear we mean $O(n^{1-\varepsilon})$ for some $\varepsilon>0$, where $n$ is the size of the active domain of the current database

Synchronization of organ pipes: experimental observations and modeling

We report measurements on the synchronization properties of organ pipes. First, we investigate influence of an external acoustical signal from a loudspeaker on the sound of an organ pipe. Second, the mutual influence of two pipes with different pitch is analyzed. In analogy to the externally driven, or mutually coupled self-sustained oscillators, one observes a frequency locking, which can be explained by synchronization theory. Further, we measure the dependence of the frequency of the signals emitted by two mutually detuned pipes with varying distance between the pipes. The spectrum shows a broad ``hump'' structure, not found for coupled oscillators. This indicates a complex coupling of the two organ pipes leading to nonlinear beat phenomena.Comment: 24 pages, 10 Figures, fully revised, 4 big figures separate in jpeg format. accepted for Journal of the Acoustical Society of Americ

An automaton over data words that captures EMSO logic

We develop a general framework for the specification and implementation of systems whose executions are words, or partial orders, over an infinite alphabet. As a model of an implementation, we introduce class register automata, a one-way automata model over words with multiple data values. Our model combines register automata and class memory automata. It has natural interpretations. In particular, it captures communicating automata with an unbounded number of processes, whose semantics can be described as a set of (dynamic) message sequence charts. On the specification side, we provide a local existential monadic second-order logic that does not impose any restriction on the number of variables. We study the realizability problem and show that every formula from that logic can be effectively, and in elementary time, translated into an equivalent class register automaton

Composition with Target Constraints

It is known that the composition of schema mappings, each specified by source-to-target tgds (st-tgds), can be specified by a second-order tgd (SO tgd). We consider the question of what happens when target constraints are allowed. Specifically, we consider the question of specifying the composition of standard schema mappings (those specified by st-tgds, target egds, and a weakly acyclic set of target tgds). We show that SO tgds, even with the assistance of arbitrary source constraints and target constraints, cannot specify in general the composition of two standard schema mappings. Therefore, we introduce source-to-target second-order dependencies (st-SO dependencies), which are similar to SO tgds, but allow equations in the conclusion. We show that st-SO dependencies (along with target egds and target tgds) are sufficient to express the composition of every finite sequence of standard schema mappings, and further, every st-SO dependency specifies such a composition. In addition to this expressive power, we show that st-SO dependencies enjoy other desirable properties. In particular, they have a polynomial-time chase that generates a universal solution. This universal solution can be used to find the certain answers to unions of conjunctive queries in polynomial time. It is easy to show that the composition of an arbitrary number of standard schema mappings is equivalent to the composition of only two standard schema mappings. We show that surprisingly, the analogous result holds also for schema mappings specified by just st-tgds (no target constraints). This is proven by showing that every SO tgd is equivalent to an unnested SO tgd (one where there is no nesting of function symbols). Similarly, we prove unnesting results for st-SO dependencies, with the same types of consequences.Comment: This paper is an extended version of: M. Arenas, R. Fagin, and A. Nash. Composition with Target Constraints. In 13th International Conference on Database Theory (ICDT), pages 129-142, 201

Game semantic analysis of equivalence in IMJ

Using game semantics, we investigate the problem of verifying contextual equivalences in Interface Middleweight Java (IMJ), an imperative object calculus in which program phrases are typed using interfaces. Working in the setting where data types are non-recursive and restricted to finite domains, we identify the frontier between decidability and undecidability by reference to the structure of interfaces present in typing judgments. In particular, we show how to determine the decidability status of problem instances (over a fixed type signature) by examining the position of methods inside the term type and the types of its free identifiers. Our results build upon the recent fully abstract game semantics of IMJ. Decidability is proved by translation into visibly pushdown register automata over infinite alphabets with fresh-input recognition

On insertion-deletion systems over relational words

We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation between their labels. We define the operations of insertion and deletion on relational words generalizing corresponding operations on strings. We prove that the transitive and reflexive closure of these operations has a decidable membership problem for the case of short insertion-deletion rules (of size two/three and three/two). At the same time, we show that in the general case such systems can produce a coding of any recursively enumerable language leading to undecidabilty of reachability questions.Comment: 24 pages, 8 figure

Regularity Problems for Visibly Pushdown Languages

International audienceVisibly pushdown automata are special pushdown automata whose stack behavior is driven by the input symbols according to a partition of the alphabet. We show that it is decidable for a given visibly pushdown automaton whether it is equivalent to a visibly counter automaton, i.e. an automaton that uses its stack only as counter. In particular, this allows to decide whether a given visibly pushdown language is a regular restriction of the set of well-matched words, meaning that the language can be accepted by a finite automaton if only well-matched words are considered as input

Earliest Query Answering for Deterministic Nested Word Automata

International audienceEarliest query answering (EQA) is an objective of many recent streaming algorithms for XML query answering, that aim for close to optimal memory management. In this paper, we show that EQA is infeasible even for a small fragment of Forward XPath except if P=NP. We then present an EQA algorithm for queries and schemas defined by deterministic nested word automata (dNWAs) and distinguish a large class of dNWAs for which streaming query answering is feasible in polynomial space and time