A Trichotomy for Regular Trail Queries

Regular path queries (RPQs) are an essential component of graph query languages. Such queries consider a regular expression r and a directed edge-labeled graph G and search for paths in G for which the sequence of labels is in the language of r. In order to avoid having to consider infinitely many paths, some database engines restrict such paths to be trails, that is, they only consider paths without repeated edges. In this paper we consider the evaluation problem for RPQs under trail semantics, in the case where the expression is fixed. We show that, in this setting, there exists a trichotomy. More precisely, the complexity of RPQ evaluation divides the regular languages into the finite languages, the class T_tract (for which the problem is tractable), and the rest. Interestingly, the tractable class in the trichotomy is larger than for the trichotomy for simple paths, discovered by Bagan et al. [Bagan et al., 2013]. In addition to this trichotomy result, we also study characterizations of the tractable class, its expressivity, the recognition problem, closure properties, and show how the decision problem can be extended to the enumeration problem, which is relevant to practice

Complex Event Processing (CEP)

Event-driven information systems demand a systematic and automatic processing of events. Complex Event Processing (CEP) encompasses methods, techniques, and tools for processing events while they occur, i.e., in a continuous and timely fashion. CEP derives valuable higher-level knowledge from lower-level events; this knowledge takes the form of so called complex events, that is, situations that can only be recognized as a combination of several events. 1 Application Areas Service Oriented Architecture (SOA), Event-Driven Architecture (EDA), cost-reductions in sensor technology and the monitoring of IT systems due to legal, contractual, or operational concerns have lead to a significantly increased generation of events in computer systems in recent years. This development is accompanied by a demand to manage and process these events in an automatic, systematic, and timely fashion. Important application areas for Complex Event Processing (CEP) are the following

Temporal Stream Algebra

Data stream management systems (DSMS) so far focus on event queries and hardly consider combined queries to both data from event streams and from a database. However, applications like emergency management require combined data stream and database queries. Further requirements are the simultaneous use of multiple timestamps after different time lines and semantics, expressive temporal relations between multiple time-stamps and exible negation, grouping and aggregation which can be controlled, i. e. started and stopped, by events and are not limited to fixed-size time windows. Current DSMS hardly address these requirements. This article proposes Temporal Stream Algebra (TSA) so as to meet the afore mentioned requirements. Temporal streams are a common abstraction of data streams and data- base relations; the operators of TSA are generalizations of the usual operators of Relational Algebra. A in-depth 'analysis of temporal relations guarantees that valid TSA expressions are non-blocking, i. e. can be evaluated incrementally. In this respect TSA differs significantly from previous algebraic approaches which use specialized operators to prevent blocking expressions on a "syntactical" level

Verification of Query Completeness over Processes [Extended Version]

Data completeness is an essential aspect of data quality, and has in turn a huge impact on the effective management of companies. For example, statistics are computed and audits are conducted in companies by implicitly placing the strong assumption that the analysed data are complete. In this work, we are interested in studying the problem of completeness of data produced by business processes, to the aim of automatically assessing whether a given database query can be answered with complete information in a certain state of the process. We formalize so-called quality-aware processes that create data in the real world and store it in the company's information system possibly at a later point.Comment: Extended version of a paper that was submitted to BPM 201

Infinite Probabilistic Databases

Probabilistic databases (PDBs) are used to model uncertainty in data in a quantitative way. In the standard formal framework, PDBs are finite probability spaces over relational database instances. It has been argued convincingly that this is not compatible with an open-world semantics (Ceylan et al., KR 2016) and with application scenarios that are modeled by continuous probability distributions (Dalvi et al., CACM 2009). We recently introduced a model of PDBs as infinite probability spaces that addresses these issues (Grohe and Lindner, PODS 2019). While that work was mainly concerned with countably infinite probability spaces, our focus here is on uncountable spaces. Such an extension is necessary to model typical continuous probability distributions that appear in many applications. However, an extension beyond countable probability spaces raises nontrivial foundational issues concerned with the measurability of events and queries and ultimately with the question whether queries have a well-defined semantics. It turns out that so-called finite point processes are the appropriate model from probability theory for dealing with probabilistic databases. This model allows us to construct suitable (uncountable) probability spaces of database instances in a systematic way. Our main technical results are measurability statements for relational algebra queries as well as aggregate queries and Datalog queries

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks