Query Order and the Polynomial Hierarchy

Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of query order, which studies the ways in which computational power is affected by the order in which information sources are accessed. The present paper studies, for the first time, query order as it applies to the levels of the polynomial hierarchy. We prove that the levels of the polynomial hierarchy are order-oblivious. Yet, we also show that these ordered query classes form new levels in the polynomial hierarchy unless the polynomial hierarchy collapses. We prove that all leaf language classes - and thus essentially all standard complexity classes - inherit all order-obliviousness results that hold for P.Comment: 14 page

Using Query Term Order for Result Summarisation

We report on two experiments performed to test the importance of Term Order in automatic summarisation. Experiment one was undertaken as part of DUC 2004 to which three systems were submitted, each with a different summarisation approach. The system that used document Term Order outperformed those that did not use Term Order in the ROUGE evaluation. Experiment two made use of human evaluations of search engine results, comparing our Query Term Order summaries with a simulation of current Google search engine result summaries in terms of summary quality. Our QTO system’s summaries aided users’ relevance judgements to a significantly greater extent than Google’s

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

On the first-order rewritability of conjunctive queries over binary guarded existential rules

We study conjunctive query answering and first-order rewritability of conjunctive queries for binary guarded existential rules. In particular, we prove that the problem of establishing whether a given set of binary guarded existential rules is such that all conjunctive queries admit a first-order rewriting is decidable, and present a technique for solving this problem. These results have a important practical impact, since they make it possible to identify those sets of binary guarded existential rules for which it is possible to answer every conjunctive query through query rewriting and standard evaluation of a first-order query (actually, a union of conjunctive queries) over a relational database system

Dynamic Complexity of Parity Exists Queries

Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman. Can this be generalised to other or even all queries that are definable in first-order logic extended by parity quantifiers? We consider the query that asks whether the number of nodes that have an edge to a red node is odd. Already this simple query of quantifier structure parity-exists is a major roadblock for dynamically capturing extensions of first-order logic. We show that this query cannot be maintained with quantifier-free first-order update rules, and that variants induce a hierarchy for such update rules with respect to the arity of the maintained auxiliary relations. Towards maintaining the query with full first-order update rules, it is shown that degree-restricted variants can be maintained