Towards Streaming Evaluation of Queries with Correlation in Complex Event Processing

Complex event processing (CEP) has gained a lot of attention for evaluating complex patterns over high-throughput data streams. Recently, new algorithms for the evaluation of CEP patterns have emerged with strong guarantees of efficiency, i.e. constant update-time per tuple and constant-delay enumeration. Unfortunately, these techniques are restricted for patterns with local filters, limiting the possibility of using joins for correlating the data of events that are far apart. In this paper, we embark on the search for efficient evaluation algorithms of CEP patterns with joins. We start by formalizing the so-called partition-by operator, a standard operator in data stream management systems to correlate contiguous events on streams. Although this operator is a restricted version of a join query, we show that partition-by (without iteration) is equally expressive as hierarchical queries, the biggest class of full conjunctive queries that can be evaluated with constant update-time and constant-delay enumeration over streams. To evaluate queries with partition-by we introduce an automata model, called chain complex event automata (chain-CEA), an extension of complex event automata that can compare data values by using equalities and disequalities. We show that this model admits determinization and is expressive enough to capture queries with partition-by. More importantly, we provide an algorithm with constant update time and constant delay enumeration for evaluating any query definable by chain-CEA, showing that all CEP queries with partition-by can be evaluated with these strong guarantees of efficiency

On the Expressiveness of Languages for Complex Event Recognition

Complex Event Recognition (CER for short) has recently gained attention as a mechanism for detecting patterns in streams of continuously arriving event data. Numerous CER systems and languages have been proposed in the literature, commonly based on combining operations from regular expressions (sequencing, iteration, and disjunction) and relational algebra (e.g., joins and filters). While these languages are naturally first-order, meaning that variables can only bind single elements, they also provide capabilities for filtering sets of events that occur inside iterative patterns; for example requiring sequences of numbers to be increasing. Unfortunately, these type of filters usually present ad-hoc syntax and under-defined semantics, precisely because variables cannot bind sets of events. As a result, CER languages that provide filtering of sequences commonly lack rigorous semantics and their expressive power is not understood. In this paper we embark on two tasks: First, to define a denotational semantics for CER that naturally allows to bind and filter sets of events; and second, to compare the expressive power of this semantics with that of CER languages that only allow for binding single events. Concretely, we introduce Set-Oriented Complex Event Logic (SO-CEL for short), a variation of the CER language introduced in [Grez et al., 2019] in which all variables bind to sets of matched events. We then compare SO-CEL with CEL, the CER language of [Grez et al., 2019] where variables bind single events. We show that they are equivalent in expressive power when restricted to unary predicates but, surprisingly, incomparable in general. Nevertheless, we show that if we restrict to sets of binary predicates, then SO-CEL is strictly more expressive than CEL. To get a better understanding of the expressive power, computational capabilities, and limitations of SO-CEL, we also investigate the relationship between SO-CEL and Complex Event Automata (CEA), a natural computational model for CER languages. We define a property on CEA called the *-property and show that, under unary predicates, SO-CEL captures precisely the subclass of CEA that satisfy this property. Finally, we identify the operations that SO-CEL is lacking to characterize CEA and introduce a natural extension of the language that captures the complete class of CEA under unary predicates

A Formal Framework for Complex Event Processing

Complex Event Processing (CEP) has emerged as the unifying field for technologies that require processing and correlating distributed data sources in real-time. CEP finds applications in diverse domains, which has resulted in a large number of proposals for expressing and processing complex events. However, existing CEP languages lack from a clear semantics, making them hard to understand and generalize. Moreover, there are no general techniques for evaluating CEP query languages with clear performance guarantees. In this paper we embark on the task of giving a rigorous and efficient framework to CEP. We propose a formal language for specifying complex events, called CEL, that contains the main features used in the literature and has a denotational and compositional semantics. We also formalize the so-called selection strategies, which had only been presented as by-design extensions to existing frameworks. With a well-defined semantics at hand, we discuss how to efficiently process complex events by evaluating CEL formulas with unary filters. We start by studying the syntactical properties of CEL and propose rewriting optimization techniques for simplifying the evaluation of formulas. Then, we introduce a formal computational model for CEP, called complex event automata (CEA), and study how to compile CEL formulas with unary filters into CEA. Furthermore, we provide efficient algorithms for evaluating CEA over event streams using constant time per event followed by constant-delay enumeration of the results. Finally, we gather the main results of this work to present an efficient and declarative framework for CEP

Ranked Enumeration of MSO Logic on Words

In the last years, enumeration algorithms with bounded delay have attracted a lot of attention for several data management tasks. Given a query and the data, the task is to preprocess the data and then enumerate all the answers to the query one by one and without repetitions. This enumeration scheme is typically useful when the solutions are treated on the fly or when we want to stop the enumeration once the pertinent solutions have been found. However, with the current schemes, there is no restriction on the order how the solutions are given and this order usually depends on the techniques used and not on the relevance for the user. In this paper we study the enumeration of monadic second order logic (MSO) over words when the solutions are ranked. We present a framework based on MSO cost functions that allows to express MSO formulae on words with a cost associated with each solution. We then demonstrate the generality of our framework which subsumes, for instance, document spanners and adds ranking to them. The main technical result of the paper is an algorithm for enumerating all the solutions of formulae in increasing order of cost efficiently, namely, with a linear preprocessing phase and logarithmic delay between solutions. The novelty of this algorithm is based on using functional data structures, in particular, by extending functional Brodal queues to suit with the ranked enumeration of MSO on words

Dynamic Data Structures for Timed Automata Acceptance

We study a variant of the classical membership problem in automata theory, which consists of deciding whether a given input word is accepted by a given automaton. We do so through the lenses of parameterized dynamic data structures: we assume that the automaton is fixed and its size is the parameter, while the input word is revealed as in a stream, one symbol at a time following the natural order on positions. The goal is to design a dynamic data structure that can be efficiently updated upon revealing the next symbol, while maintaining the answer to the query on whether the word consisting of symbols revealed so far is accepted by the automaton. We provide complexity bounds for this dynamic acceptance problem for timed automata that process symbols interleaved with time spans. The main contribution is a dynamic data structure that maintains acceptance of a fixed one-clock timed automaton ? with amortized update time 2^{?(|?|)} per input symbol

Global phylogeography and ancient evolution of the widespread human gut virus crAssphage

Microbiomes are vast communities of microorganisms and viruses that populate all natural ecosystems. Viruses have been considered to be the most variable component of microbiomes, as supported by virome surveys and examples of high genomic mosaicism. However, recent evidence suggests that the human gut virome is remarkably stable compared with that of other environments. Here, we investigate the origin, evolution and epidemiology of crAssphage, a widespread human gut virus. Through a global collaboration, we obtained DNA sequences of crAssphage from more than one-third of the world's countries and showed that the phylogeography of crAssphage is locally clustered within countries, cities and individuals. We also found fully colinear crAssphage-like genomes in both Old-World and New-World primates, suggesting that the association of crAssphage with primates may be millions of years old. Finally, by exploiting a large cohort of more than 1,000 individuals, we tested whether crAssphage is associated with bacterial taxonomic groups of the gut microbiome, diverse human health parameters and a wide range of dietary factors. We identified strong correlations with different clades of bacteria that are related to Bacteroidetes and weak associations with several diet categories, but no significant association with health or disease. We conclude that crAssphage is a benign cosmopolitan virus that may have coevolved with the human lineage and is an integral part of the normal human gut virome