Polynomial Data Complexity Research Articles

Enumerating grammar-based extractions

We propose a new grammar-based language for defining information extractors from documents (text) that is built upon the well-studied framework of document spanners for extracting structured data from text. While previously studied formalisms for document spanners are mainly based on regular expressions, we use an extension of context-free grammars, called extraction grammars, to define the new class of context-free spanners. Extraction grammars are simply context-free grammars extended with variables that capture interval positions of the document, namely spans. While regular expressions are efficient for tokenizing and tagging, context-free grammars are also efficient for capturing structural properties. Indeed, we show that context-free spanners are strictly more expressive than their regular counterparts. We reason about the expressive power of our new class and present a pushdown-automata model that captures it. We show that extraction grammars can be evaluated with polynomial data complexity. Nevertheless, as the degree of the polynomial depends on the query, we present an enumeration algorithm for unambiguous extraction grammars that, after quintic preprocessing, outputs the results sequentially, without repetitions, with a constant delay between every two consecutive ones.

On the Complexity of Consistent Query Answering in the Presence of Simple Ontologies

Consistent query answering is a standard approach for producing meaningful query answers when data is inconsistent. Recent work on consistent query answering in the presence of ontologies has shown this problem to be intractable in data complexity even for ontologies expressed in lightweight description logics. In order to better understand the source of this intractability, we investigate the complexity of consistent query answering for simple ontologies consisting only of class subsumption and class disjointness axioms. We show that for conjunctive queries with at most one quantified variable, the problem is first-order expressible; for queries with at most two quantified variables, the problem has polynomial data complexity but may not be first-order expressible; and for three quantified variables, the problem may become co-NP-hard in data complexity. For queries having at most two quantified variables, we further identify a necessary and sufficient condition for first-order expressibility. In order to be able to handle arbitrary conjunctive queries, we propose a novel inconsistency-tolerant semantics and show that under this semantics, first-order expressibility is always guaranteed. We conclude by extending our positive results to DL-Lite ontologies without inverse.

Security Analysis of A Stream Cipher with Proven Properties

Si and Ding proposed a stream cipher with two keys (the first and the second key) and an expected security strength. To further measure the security, we analyze the stream cipher by considering the selective discrete Fourier spectra attack and the fast selective discrete Fourier spectra attack. The two attacks reveal a fact that the second key is more important than the first key, that is, if the second key is leaked out, the first key can be obtained with a lower time complexity than that of the expected security. In addition, we analyze the ability of the stream cipher to resist the guess-anddetermine attack. The results show an attacker is able to gain the two keys with an exponentially improved time complexity and a polynomial data complexity. It implies that we need a securer permutation over finite fields to design a new binary additive stream cipher to achieve the expected security level.

Data Access With Horn Ontologies: Where Description Logics Meet Existential Rules

Two main families of ontology languages are considered in the context of data access, namely Horn description logics and existential rules. In this paper, we review the semantic relationships between these families in the light of the ontology-mediated query answering problem. To this end, we rely on the standard translation of description logics in first-order logic and on the notion of semantic emulation. We focus on description logics and classes of existential rules for which the con-junctive query answering problem has polynomial data complexity.

Efficient provenance tracking for datalog using top-k queries

Highly expressive declarative languages, such as datalog, are now commonly used to model the operational logic of data-intensive applications. The typical complexity of such datalog programs, and the large volume of data that they process, call for result explanation. Results may be explained through the tracking and presentation of data provenance, defined here as the set of derivation trees of a given fact. While informative, the size of such full provenance information is typically too large and complex (even when compactly represented) to allow displaying it to the user. To this end, we propose a novel top-k query language for querying datalog provenance, supporting selection criteria based on tree patterns and ranking based on the rules and database facts used in derivation. We propose an efficient novel algorithm that computes in polynomial data complexity a compact representation of the top-k trees which may be explicitly constructed in linear time with respect to their size. We further experimentally study the algorithm performance, showing its scalability even for complex datalog programs where full provenance tracking is infeasible.

Selective provenance for datalog programs using top-k queries

Highly expressive declarative languages, such asdatalog, are now commonly used to model the operational logic of data-intensive applications. The typical complexity of such datalog programs, and the large volume of data that they process, call for resultexplanation.Results may be explained through the tracking and presentation ofdata provenance, and here we focus on a detailed form of provenance (how-provenance), defining it as the set of derivation trees of a given fact. While informative, the size of suchfullprovenance information is typically too large and complex (even when compactly represented) to allow displaying it to the user. To this end, we propose a novel top-k query language for querying datalog provenance, supporting selection criteria based on tree patterns and ranking based on the rules and database facts used in derivation. We propose an efficient novel algorithm based on (1) instrumenting the datalog program so that, upon evaluation, it generates only relevant provenance, and (2) efficient top-k (relevant) provenance generation, combined with bottom-up datalog evaluation. The algorithm computes in polynomial data complexity a compact representation of the top-k trees which may be explicitly constructed in linear time with respect to their size. We further experimentally study the algorithm performance, showing its scalability even for complex datalog programs where full provenance tracking is infeasible.

Towards richer rule languages with polynomial data complexity for the Semantic Web

We introduce a Horn description logic called Horn-DL, which is strictly and essentially richer than Horn‐RegI, Horn‐SHIQ and Horn‐SROIQ, while still has PTime data complexity. In comparison with Horn‐SROIQ, Horn-DL additionally allows the universal role and assertions of the form irreflexives, ¬s(a, b), a≠˙b. More importantly, in contrast to all the well-known Horn fragments EL, DL-Lite, DLP, Horn‐SHIQ, and Horn‐SROIQ of description logics, Horn-DL allows a form of the concept constructor “universal restriction” to appear at the left hand side of terminological inclusion axioms. Namely, a universal restriction can be used in such places in conjunction with the corresponding existential restriction. We develop the first algorithm with PTime data complexity for checking satisfiability of Horn-DL knowledge bases.

Query-Driven Procedures for Hybrid MKNF Knowledge Bases

Hybrid MKNF knowledge bases are one of the most prominent tightly integrated combinations of open-world ontology languages with closed-world (nonmonotonic) rule paradigms. Based on the logic of minimal knowledge and negation as failure (MKNF), the definition of Hybrid MKNF is parametric on the description logic (DL) underlying the ontology language, in the sense that nonmonotonic rules can extend any decidable DL language. Two related semantics have been defined for Hybrid MKNF: one that is based on the Stable Model Semantics for logic programs and one on the Well-Founded Semantics (WFS). Under WFS, the definition of Hybrid MKNF relies on a bottom-up computation that has polynomial data complexity whenever the DL language is tractable. Here we define a general query-driven procedure for Hybrid MKNF that is sound with respect to the stable model-based semantics, and sound and complete with respect to its WFS variant. This procedure is able to answer a slightly restricted form of conjunctive queries, and is based on tabled rule evaluation extended with an external oracle that captures reasoning within the ontology. Such an (abstract) oracle receives as input a query along with knowledge already derived, and replies with a (possibly empty) set of atoms, defined in the rules, whose truth would suffice to prove the initial query. With appropriate assumptions on the complexity of the abstract oracle, the general procedure maintains the data complexity of the WFS for Hybrid MKNF knowledge bases. To illustrate this approach, we provide a concrete oracle for EL + , a fragment of the lightweight DL EL ++ . Such an oracle has practical use, as EL ++ is the language underlying OWL 2 EL, which is part of the W3C recommendations for the Semantic Web, and is tractable for reasoning tasks such as subsumption. We show that query-driven Hybrid MKNF preserves polynomial data complexity when using the EL + oracle and WFS.

A structural/temporal query language for Business Processes

A Business Process consists of multiple business activities, which, when combined in a flow, achieve some particular goal. These processes usually operate in a distributed environment and the software implementing them is fairly complex. Thus, effective tools for analysis of the possible executions of such processes are extremely important for companies (Beeri et al., 2006, 2007 [4,5]); (Deutch and Milo, 2008 [13]); these tools can allow to debug and optimize the processes, and to make an optimal use of them. The goal of the present paper is to consider a formal model underlying Business Processes and study query languages over such processes. We study in details the relationship of the proposed model with previously suggested formalisms for processes modeling and querying. In particular we propose a query evaluation algorithm of polynomial data complexity that can be applied uniformly to two kind of common queries over processes, namely queries on the structure of the process specification as well as temporal queries on the potential behavior of the defined process. We show that unless P = N P the efficiency of our algorithm is asymptotically optimal.

Well-founded semantics for description logic programs in the semantic web

The realization of the Semantic Web vision, in which computational logic has a prominent role, has stimulated a lot of research on combining rules and ontologies, which are formulated in different formalisms. In particular, combining logic programming with the Web Ontology Language (OWL), which is a standard based on description logics, emerged as an important issue for linking the Rules and Ontology Layers of the Semantic Web. Nonmonotonic description logic programs (dl-programs) were introduced for such a combination, in which a pair(L,P)of a description logic knowledge baseLand a set of rulesPwith negation as failure is given a model-based semantics that generalizes the answer set semantics of logic programs. In this article, we reconsider dl-programs and present a well-founded semantics for them as an analog for the other main semantics of logic programs. It generalizes the canonical definition of the well-founded semantics based on unfounded sets, and, as we show, lifts many of the well-known properties from ordinary logic programs to dl-programs. Among these properties, our semantics amounts to a partial model approximating the answer set semantics, which yields for positive and stratified dl-programs, a total model coinciding with the answer set semantics; it has polynomial data complexity provided the access to the description logic knowledge base is polynomial; under suitable restrictions, it has lower complexity and even first-order rewritability is achievable. The results add to previous evidence that dl-programs are a versatile and robust combination approach, which moreover is implementable using legacy engines.

Querying over fuzzy description logic

Description logics (DLs) play an important role in representing and reasoning domain knowledge. Conjunctive queries stemmed from the domain of relational databases, and have attracted more attentions in semantic Web recently. To acquire a tractable DL for query answering, DL-Lite is proposed. Due to the large amount of imprecision and uncertainty in the real world, it is essential to extend DLs to deal with these vague and imprecise information. We thus propose a new fuzzy DL f-DLR-Liteℱ⊓, which allows for the presence of n-ary relations and the occurrence of concept conjunction on the left land of inclusion axioms. We also suggest an improved fuzzy query language, which supports the presence of thresholds and user defined weights. We also show that the query answering algorithm over the extended DL is still FOL reducible and shows polynomial data complexity. DL f-DLR-Liteℱ⊓ can make up for the disadvantages of knowledge representation and reasoning of classic DLs, and the enhanced query language expresses user intentions more precisely and reasonably.

Reasoning in Description Logics by a Reduction to Disjunctive Datalog

As applications of description logics proliferate, efficient reasoning with knowledge bases containing many assertions becomes ever more important. For such cases, we developed a novel reasoning algorithm that reduces a $\mathcal{SHIQ}$ knowledge base to a disjunctive datalog program while preserving the set of ground consequences. Queries can then be answered in the resulting program while reusing existing and practically proven optimization techniques of deductive databases, such as join-order optimizations or magic sets. Moreover, we use our algorithm to derive precise data complexity bounds: we show that $\mathcal{SHIQ}$ is data complete for NP, and we identify an expressive fragment of $\mathcal{SHIQ}$ with polynomial data complexity.

Tabling for non-monotonic programming

Nondmonotonic extensions add power to logic programs. However, the main logic programming language, Prolog, is widely recognized as inadequate to implement these extensions due to its weak termination and complexity properties. By extending Prolog’s SLD resolution with tabling, Prolog can be improved in several ways. Tabling can allow a logic programming system to compute the welldfounded semantics for programs with bounded term depth, and to do so with polynomial data complexity. By exploiting these properties, tabling allows a variety of nondmonotonic extensions to be efficiently implemented, and used to solve practical problems. In this paper we describe tabling as it is implemented in the XSB system and show how it can be used to construct metadinterpreters (or preprocessors) for two sample formalisms: the WelldFounded Semantics with Explicit Negation, and Generalized Annotated Logic Programs. We also describe how nondmonotonic extensions are used in practical applications such as psychiatric diagnosis, extraction of information from poorly structured textual data, and model checking.

A nondeterministic well-founded semantics

In order to define the meaning of a collection of rules forming a database or logic program, we have to consider a number of alternative interpretations. In the case of stratified and locally stratified programs, researchers agree that a single such interpretation captures the intended semantics [16]. Nevertheless, nonstratified datalog databases and logic programs can be seen as descriptions of a set of “alternative scenarios”. Sacca and Zaniolo [20] have shown that the nondeterministic nature of these programs can be used to model several useful queries such as those involving thechoice operator. They introducedpartial stable models, a semantics that exhibits the desired nondeterministic behavior. This work opened the problem of finding efficient ways to compute these nondeterministic scenarios. Papadimitriou and Yannakakis [18] introduced a tie-breaking procedure that nondeterministically computes fixpoints for some programs and has polynomial data complexity. However, this algorithm does not handle many programs includingchoice programs. In this paper, we introduce the notion ofwell-founded hypothesis, an intuitive account based on hypothetical reasoning that captures the same semantics as Sacca and Zaniolo's partial stable models. We introduce a notion of linearity that can be used in a skeptical or nondeterministic fashion. We show that the skeptical case corresponds to thewell-founded semantics and that the nondeterministic case computes a sound subclass of well-founded hypotheses. We show that this latter subclass has polynomial data complexity, correctly handleschoice programs, and is universally defined. We develop a simple nondeterministic procedure that computes these linear hypotheses, and we extend it to compute a strict superclass of the well-founded tie-breaking fixpoints in polynomial time.

XSB as an efficient deductive database engine

This paper describes the XSB system, and its use as an in-memory deductive database engine. XSB began from a Prolog foundation, and traditional Prolog systems are known to have serious deficiencies when used as database systems. Accordingly, XSB has a fundamental bottom-up extension, introduced through tabling (or memoing)[4], which makes it appropriate as an underlying query engine for deductive database systems. Because it eliminates redundant computation, the tabling extension makes XSB able to compute all modularly stratified datalog programs finitely and with polynomial data complexity. For non-stratified programs, a meta-interpreter with the same properties is provided. In addition XSB significantly extends and improves the indexing capabilities over those of standard Prolog. Finally, its syntactic basis in HiLog [2], lends it flexibility for data modelling. The implementation of XSB derives from the WAM [25], the most common Prolog engine. XSB inherits the WAM's efficiency and can take advantage of extensive compiler technology developed for Prolog. As a result, performance comparisons indicate that XSB is significantly faster than other deductive database systems for a wide range of queries and stratified rule sets. XSB is under continuous development, and version 1.3 is available through anonymous ftp.

Interpreting a reconstructed relational calculus (extended abstract)

This paper describes a method for answering all relational calculus queries under the assumption that the domain of data values is sufficiently large. The method extends recent theoretical results that use extended relation representations to answer domain dependent queries, without the use of auxilliary variables or invented constants or an explicit enumeration of the active domain. The method is shown to be logically correct and to have polynomial data complexity. By identifying relational algebra operations with relational calculus queries this approach extends relational algebra to a full boolean algebra, where intersection, union, and difference are defined between any two relations, whether or not they are union compatible. An example illustrates that this approach can be useful in distributed query optimization.

On the representation and querying of sets of possible worlds

We represent a set of possible worlds using an incomplete information database. The representation techniques that we study form a hierarchy, which generalizes relations of constants. This hierarchy ranges from the very simple Codd-table, (i e , a relation of constants and distinct variables called nulls, which stand for values present but unknown), to much more complex mechanisms involving views on conditioned-tables, (i e , queries on Codd-tables together with conditions). The views we consider are the queries that have polynomial data-complexity on complete information databases. Our conditions are conjunctions of equalities and inequalities. (1) We provide matching upper and lower bounds on the data-complexity of testing containement , membership , and uniqueness for sets of possible worlds and we fully classify these problems with respect to our representation hierarchy. The most surprising result in this classification is that it is complete in Π 2 p , whether a set of possible worlds represented by a Codd-table is a subset of a set of possible worlds represented by a Codd-table with one conjuction of inequalities. (2) We investigate the data-complexity of querying incomplete information databases. We examine both asking for certain facts and for possible facts . Our approach is algebraic but our bounds also apply to logical databases. We show that asking for a certain fact is coNP-complete, even for a fixed first order query on a Codd-table. We thus strengthen a lower bound of [16], who showed that this holds for a Codd-table with a conjunction of inequalities. For each fixed positive existential query we present a polynomial algorithm solving the bounded possible fact problem of this query on conditioned-tables. We show that our approach is, in a sense, the best possible, by deriving two NP-completeness lower bounds for the bounded possible fact problem when the fixed query contains either negation or recursion.