arXiv subjects

Cristian Riveros

Publications and source records attributed to Cristian Riveros.

32 records · Page 2Linked to original sources

arXiv2021

MillenniumDB: A Persistent, Open-Source, Graph Database

In this systems paper, we present MillenniumDB: a novel graph database engine that is modular, persistent, and open source. MillenniumDB is based on a graph data model, which we call domain graphs, that provides a simple abstraction upon which a variety of popular graph models can be supported. The engine itself is founded on a combination of tried and tested techniques from relational data management, state-of-the-art algorithms for worst-case-optimal joins, as well as graph-specific algorithms for evaluating path queries. In this paper, we present the main design principles underlying MillenniumDB, describing the abstract graph model and query semantics supported, the concrete data model and query syntax implemented, as well as the storage, indexing, query planning and query evaluation techniques used. We evaluate MillenniumDB over real-world data and queries from the Wikidata knowledge graph, where we find that it outperforms other popular persistent graph database engines (including both enterprise and open source alternatives) that support similar query features.

cs.DB↗

arXiv2021

Pumping lemmas for weighted automata

We present pumping lemmas for five classes of functions definable by fragments of weighted automata over the min-plus semiring, the max-plus semiring and the semiring of natural numbers. As a corollary we show that the hierarchy of functions definable by unambiguous, finitely-ambiguous, polynomially-ambiguous weighted automata, and the full class of weighted automata is strict for the min-plus and max-plus semirings.

cs.LO↗

arXiv2021

$\text{#NFA}$ admits an FPRAS: Efficient Enumeration, Counting, and Uniform Generation for Logspace Classes

In this work, we study two simple yet general complexity classes, based on logspace Turing machines, which provide a unifying framework for efficient query evaluation in areas like information extraction and graph databases, among others. We investigate the complexity of three fundamental algorithmic problems for these classes: enumeration, counting and uniform generation of solutions, and show that they have several desirable properties in this respect. Both complexity classes are defined in terms of non-deterministic logspace transducers (NL transducers). For the first class, we consider the case of unambiguous NL transducers, and we prove constant delay enumeration, and both counting and uniform generation of solutions in polynomial time. For the second class, we consider unrestricted NL transducers, and we obtain polynomial delay enumeration, approximate counting in polynomial time, and polynomial-time randomized algorithms for uniform generation. More specifically, we show that each problem in this second class admits a fully polynomial-time randomized approximation scheme (FPRAS) and a polynomial-time Las Vegas algorithm for uniform generation. Interestingly, the key idea to prove these results is to show that the fundamental problem $\text{#NFA}$ admits an FPRAS, where $\text{#NFA}$ is the problem of counting the number of strings of length $n$ (given in unary) accepted by a non-deterministic finite automaton (NFA). While this problem is known to be $\text{#P}$-complete and, more precisely, $\text{SpanL}$-complete, it was open whether this problem admits an FPRAS. In this work, we solve this open problem, and obtain as a welcome corollary that every function in $\text{SpanL}$ admits an FPRAS.

cs.DS↗

arXiv2020

When is Approximate Counting for Conjunctive Queries Tractable?

Conjunctive queries are one of the most common class of queries used in database systems, and the best studied in the literature. A seminal result of Grohe, Schwentick, and Segoufin (STOC 2001) demonstrates that for every class $G$ of graphs, the evaluation of all conjunctive queries whose underlying graph is in $G$ is tractable if, and only if, $G$ has bounded treewidth. In this work, we extend this characterization to the counting problem for conjunctive queries. Specifically, for every class $C$ of conjunctive queries with bounded treewidth, we introduce the first fully polynomial-time randomized approximation scheme (FPRAS) for counting answers to a query in $C$, and the first polynomial-time algorithm for sampling answers uniformly from a query in $C$. As a corollary, it follows that for every class $G$ of graphs, the counting problem for conjunctive queries whose underlying graph is in $G$ admits an FPRAS if, and only if, $G$ has bounded treewidth (unless $\text{BPP} \neq \text{P}$)}. In fact, our FPRAS is more general, and also applies to conjunctive queries with bounded hypertree width, as well as unions of such queries. The key ingredient in our proof is the resolution of a fundamental counting problem from automata theory. Specifically, we demonstrate the first FPRAS and polynomial time sampler for the set of trees of size $n$ accepted by a tree automaton, which improves the prior quasi-polynomial time randomized approximation scheme (QPRAS) and sampling algorithm of Gore, Jerrum, Kannan, Sweedyk, and Mahaney '97. We demonstrate how this algorithm can be used to obtain an FPRAS for many hitherto open problems, such as counting solutions to constraint satisfaction problems (CSP) with bounded hypertree-width, counting the number of error threads in programs with nested call subroutines, and counting valid assignments to structured DNNF circuits.

cs.DS↗

arXiv2020

Expressive power of linear algebra query languages

Linear algebra algorithms often require some sort of iteration or recursion as is illustrated by standard algorithms for Gaussian elimination, matrix inversion, and transitive closure. A key characteristic shared by these algorithms is that they allow looping for a number of steps that is bounded by the matrix dimension. In this paper we extend the matrix query language MATLANG with this type of recursion, and show that this suffices to express classical linear algebra algorithms. We study the expressive power of this language and show that it naturally corresponds to arithmetic circuit families, which are often said to capture linear algebra. Furthermore, we analyze several sub-fragments of our language, and show that their expressive power is closely tied to logical formalisms on semiring-annotated relations.

cs.CC↗

arXiv2020

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 regular complex event processing queries 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.

cs.FL↗

arXiv2020

The monitoring problem for timed automata

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 under a different perspective, that is, we consider a dynamic version of the problem, called monitoring problem, where the automaton is fixed and the input is revealed as in a stream, one symbol at a time following the natural order on positions. The goal here is to design a dynamic data structure that can be queried about whether the word consisting of symbols revealed so far is accepted by the automaton, and that can be efficiently updated when the next symbol is revealed. We provide complexity bounds for this monitoring problem, by considering timed automata that process symbols interleaved with timestamps. The main contribution is that monitoring of a one-clock timed automaton, with all its components but the clock constants fixed, can be done in amortised constant time per input symbol.

cs.FL↗

arXiv2020

Descriptive Complexity for Counting Complexity Classes

Descriptive Complexity has been very successful in characterizing complexity classes of decision problems in terms of the properties definable in some logics. However, descriptive complexity for counting complexity classes, such as FP and #P, has not been systematically studied, and it is not as developed as its decision counterpart. In this paper, we propose a framework based on Weighted Logics to address this issue. Specifically, by focusing on the natural numbers we obtain a logic called Quantitative Second Order Logics (QSO), and show how some of its fragments can be used to capture fundamental counting complexity classes such as FP, #P and FPSPACE, among others. We also use QSO to define a hierarchy inside #P, identifying counting complexity classes with good closure and approximation properties, and which admit natural complete problems. Finally, we add recursion to QSO, and show how this extension naturally captures lower counting complexity classes such as #L.

cs.LO↗

arXiv2018

Foundations of 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 study how to efficiently evaluate CEL for processing complex events in the case of 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 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. By gathering these results together, we propose a framework for efficiently evaluating CEL with unary filters. Finally, we show experimentally that this framework consistently outperforms the competition, and even over trivial queries can be orders of magnitude more efficient.

cs.DB↗

arXiv2018

Copyless Cost-Register Automata: Structure, Expressiveness, and Closure Properties

Cost register automata (CRA) and its subclass, copyless CRA, were recently proposed by Alur et al. as a new model for computing functions over strings. We study some structural properties, expressiveness, and closure properties of copyless CRA. We show that copyless CRA are strictly less expressive than weighted automata and are not closed under reverse operation. To find a better class we impose restrictions on copyless CRA, which ends successfully with a new robust computational model that is closed under reverse and other extensions.

cs.FL↗

arXiv2018

Constant delay algorithms for regular document spanners

Regular expressions and automata models with capture variables are core tools in rule-based information extraction. These formalisms, also called regular document spanners, use regular languages in order to locate the data that a user wants to extract from a text document, and then store this data into variables. Since document spanners can easily generate large outputs, it is important to have good evaluation algorithms that can generate the extracted data in a quick succession, and with relatively little precomputation time. Towards this goal, we present a practical evaluation algorithm that allows constant delay enumeration of a spanner's output after a precomputation phase that is linear in the document. While the algorithm assumes that the spanner is specified in a syntactic variant of variable set automata, we also study how it can be applied when the spanner is specified by general variable set automata, regex formulas, or spanner algebras. Finally, we study the related problem of counting the number of outputs of a document spanner, providing a fine grained analysis of the classes of document spanners that support efficient enumeration of their results.

cs.DB↗

arXiv2017

Document Spanners for Extracting Incomplete Information: Expressiveness and Complexity

Rule-based information extraction has lately received a fair amount of attention from the database community, with several languages appearing in the last few years. Although information extraction systems are intended to deal with semistructured data, all language proposals introduced so far are designed to output relations, thus making them incapable of handling incomplete information. To remedy the situation, we propose to extend information extraction languages with the ability to use mappings, thus allowing us to work with documents which have missing or optional parts. Using this approach, we simplify the semantics of regex formulas and extraction rules, two previously defined methods for extracting information, extend them with the ability to handle incomplete data, and study how they compare in terms of expressive power. We also study computational properties of these languages, focusing on the query enumeration problem, as well as satisfiability and containment.

cs.DB↗

arXiv2017

A Second-Order Approach to Complex Event Recognition

Complex Event Recognition (CER for short) refers to the activity of detecting patterns in streams of continuously arriving data. This field has been traditionally approached from a practical point of view, resulting in heterogeneous implementations with fundamentally different capabilities. The main reason behind this is that defining formal semantics for a CER language is not trivial: they usually combine first-order variables for joining and filtering events with regular operators like sequencing and Kleene closure. Moreover, their semantics usually focus only on the detection of complex events, leaving the concept of output mostly unattended. In this paper, we propose to unify the semantics and output of complex event recognition languages by using second order objects. Specifically, we introduce a CER language called Second Order Complex Event Logic (SO-CEL for short), that uses second order variables for managing and outputting sequences of events. This makes the definition of the main CER operators simple, allowing us to develop the first steps in understanding its expressive power. We start by comparing SO-CEL with a version that uses first-order variables called FO-CEL, showing 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 FO-CEL. Then, we introduce a natural computational model called Unary Complex Event Automata (UCEA) that provides a better understanding of SO-CEL. We show that, under unary predicates, SO-CEL captures the subclass of UCEA that satisfy the so-called *-property. Finally, we identify the operations that SO-CEL is lacking to capture UCEA and introduce a natural extension of the language that captures the complete class of UCEA under unary predicates.

cs.DB↗

arXiv2010

Composition and Inversion of Schema Mappings

In the recent years, a lot of attention has been paid to the development of solid foundations for the composition and inversion of schema mappings. In this paper, we review the proposals for the semantics of these crucial operators. For each of these proposals, we concentrate on the three following problems: the definition of the semantics of the operator, the language needed to express the operator, and the algorithmic issues associated to the problem of computing the operator. It should be pointed out that we primarily consider the formalization of schema mappings introduced in the work on data exchange. In particular, when studying the problem of computing the composition and inverse of a schema mapping, we will be mostly interested in computing these operators for mappings specified by source-to-target tuple-generating dependencies.

cs.DB↗