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Thomas Schwentick

Publications and source records attributed to Thomas Schwentick.

32 records · Page 2Linked to original sources
arXiv2014

Games for Active XML Revisited

The paper studies the rewriting mechanisms for intensional documents in the Active XML framework, abstracted in the form of active context-free games. The safe rewriting problem studied in this paper is to decide whether the first player, Juliet, has a winning strategy for a given game and (nested) word; this corresponds to a successful rewriting strategy for a given intensional document. The paper examines several extensions to active context-free games. The primary extension allows more expressive schemas (namely XML schemas and regular nested word languages) for both target and replacement languages and has the effect that games are played on nested words instead of (flat) words as in previous studies. Other extensions consider validation of input parameters of web services, and an alternative semantics based on insertion of service call results. In general, the complexity of the safe rewriting problem is highly intractable (doubly exponential time), but the paper identifies interesting tractable cases.

cs.DB↗
arXiv2012

On optimum left-to-right strategies for active context-free games

Active context-free games are two-player games on strings over finite alphabets with one player trying to rewrite the input string to match a target specification. These games have been investigated in the context of exchanging Active XML (AXML) data. While it was known that the rewriting problem is undecidable in general, it is shown here that it is EXPSPACE-complete to decide for a given context-free game, whether all safely rewritable strings can be safely rewritten in a left-to-right manner, a problem that was previously considered by Abiteboul et al. Furthermore, it is shown that the corresponding problem for games with finite replacement languages is EXPTIME-complete.

cs.DB↗
arXiv2012

Two-Variable Logic with Two Order Relations

It is shown that the finite satisfiability problem for two-variable logic over structures with one total preorder relation, its induced successor relation, one linear order relation and some further unary relations is EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures that do not include the induced successor relation. As a special case, the EXPSPACE upper bound applies to two-variable logic over structures with two linear orders. A further consequence is that satisfiability of two-variable logic over data words with a linear order on positions and a linear order and successor relation on the data is decidable in EXPSPACE. As a complementing result, it is shown that over structures with two total preorder relations as well as over structures with one total preorder and two linear order relations, the finite satisfiability problem for two-variable logic is undecidable.

cs.LO↗
arXiv2011

A note on the expressive power of linear orders

This article shows that there exist two particular linear orders such that first-order logic with these two linear orders has the same expressive power as first-order logic with the Bit-predicate FO(Bit). As a corollary we obtain that there also exists a built-in permutation such that first-order logic with a linear order and this permutation is as expressive as FO(Bit).

cs.LO↗
arXiv2011

Feasible Automata for Two-Variable Logic with Successor on Data Words

We introduce an automata model for data words, that is words that carry at each position a symbol from a finite alphabet and a value from an unbounded data domain. The model is (semantically) a restriction of data automata, introduced by Bojanczyk, et. al. in 2006, therefore it is called weak data automata. It is strictly less expressive than data automata and the expressive power is incomparable with register automata. The expressive power of weak data automata corresponds exactly to existential monadic second order logic with successor +1 and data value equality \sim, EMSO2(+1,\sim). It follows from previous work, David, et. al. in 2010, that the nonemptiness problem for weak data automata can be decided in 2-NEXPTIME. Furthermore, we study weak Büchi automata on data omega-strings. They can be characterized by the extension of EMSO2(+1,\sim) with existential quantifiers for infinite sets. Finally, the same complexity bound for its nonemptiness problem is established by a nondeterministic polynomial time reduction to the nonemptiness problem of weak data automata.

cs.FL↗
arXiv2011

Rewriting Ontological Queries into Small Nonrecursive Datalog Programs

We consider the setting of ontological database access, where an Abox is given in form of a relational database D and where a Boolean conjunctive query q has to be evaluated against D modulo a Tbox T formulated in DL-Lite or Linear Datalog+/-. It is well-known that (T,q) can be rewritten into an equivalent nonrecursive Datalog program P that can be directly evaluated over D. However, for Linear Datalog? or for DL-Lite versions that allow for role inclusion, the rewriting methods described so far result in a nonrecursive Datalog program P of size exponential in the joint size of T and q. This gives rise to the interesting question of whether such a rewriting necessarily needs to be of exponential size. In this paper we show that it is actually possible to translate (T,q) into a polynomially sized equivalent nonrecursive Datalog program P.

cs.AI↗
arXiv2010

Temporal Logics on Words with Multiple Data Values

The paper proposes and studies temporal logics for attributed words, that is, data words with a (finite) set of (attribute,value)-pairs at each position. It considers a basic logic which is a semantical fragment of the logic $LTL^\downarrow_1$ of Demri and Lazic with operators for navigation into the future and the past. By reduction to the emptiness problem for data automata it is shown that this basic logic is decidable. Whereas the basic logic only allows navigation to positions where a fixed data value occurs, extensions are studied that also allow navigation to positions with different data values. Besides some undecidable results it is shown that the extension by a certain UNTIL-operator with an inequality target condition remains decidable.

cs.LO↗
arXiv2009

On the Hybrid Extension of CTL and CTL+

The paper studies the expressivity, relative succinctness and complexity of satisfiability for hybrid extensions of the branching-time logics CTL and CTL+ by variables. Previous complexity results show that only fragments with one variable do have elementary complexity. It is shown that H1CTL+ and H1CTL, the hybrid extensions with one variable of CTL+ and CTL, respectively, are expressively equivalent but H1CTL+ is exponentially more succinct than H1CTL. On the other hand, HCTL+, the hybrid extension of CTL with arbitrarily many variables does not capture CTL*, as it even cannot express the simple CTL* property EGFp. The satisfiability problem for H1CTL+ is complete for triply exponential time, this remains true for quite weak fragments and quite strong extensions of the logic.

cs.LO↗
arXiv2008

Dynamic Complexity of Formal Languages

The paper investigates the power of the dynamic complexity classes DynFO, DynQF and DynPROP over string languages. The latter two classes contain problems that can be maintained using quantifier-free first-order updates, with and without auxiliary functions, respectively. It is shown that the languages maintainable in DynPROP exactly are the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for DynPROP and separates DynPROP from DynQF and DynFO. Further, it is shown that any context-free language can be maintained in DynFO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in DynQF. Furthermore, the dynamic complexity of regular tree languages is investigated and some results concerning arbitrary structures are obtained: there exist first-order definable properties which are not maintainable in DynPROP. On the other hand any existential first-order property can be maintained in DynQF when allowing precomputation.

cs.CC↗
arXiv2008

Complexity of Hybrid Logics over Transitive Frames

This paper examines the complexity of hybrid logics over transitive frames, transitive trees, and linear frames. We show that satisfiability over transitive frames for the hybrid language extended with the downarrow operator is NEXPTIME-complete. This is in contrast to undecidability of satisfiability over arbitrary frames for this language (Areces, Blackburn, Marx 1999). It is also shown that adding the @ operator or the past modality leads to undecidability over transitive frames. This is again in contrast to the case of transitive trees and linear frames, where we show these languages to be nonelementarily decidable. Moreover, we establish 2EXPTIME and EXPTIME upper bounds for satisfiability over transitive frames and transitive trees, respectively, for the hybrid Until/Since language. An EXPTIME lower bound is shown to hold for the modal Until language over both frame classes.

cs.LO↗
arXiv2006

On the complexity of XPath containment in the presence of disjunction, DTDs, and variables

XPath is a simple language for navigating an XML-tree and returning a set of answer nodes. The focus in this paper is on the complexity of the containment problem for various fragments of XPath. We restrict attention to the most common XPath expressions which navigate along the child and/or descendant axis. In addition to basic expressions using only node tests and simple predicates, we also consider disjunction and variables (ranging over nodes). Further, we investigate the containment problem relative to a given DTD. With respect to variables we study two semantics, (1) the original semantics of XPath, where the values of variables are given by an outer context, and (2) an existential semantics introduced by Deutsch and Tannen, in which the values of variables are existentially quantified. In this framework, we establish an exact classification of the complexity of the containment problem for many XPath fragments.

cs.DB↗
arXiv2003

Solving equations in the relational algebra

Enumerating all solutions of a relational algebra equation is a natural and powerful operation which, when added as a query language primitive to the nested relational algebra, yields a query language for nested relational databases, equivalent to the well-known powerset algebra. We study \emph{sparse} equations, which are equations with at most polynomially many solutions. We look at their complexity, and compare their expressive power with that of similar notions in the powerset algebra.

cs.LO↗
arXiv1998

The descriptive complexity approach to LOGCFL

Building upon the known generalized-quantifier-based first-order characterization of LOGCFL, we lay the groundwork for a deeper investigation. Specifically, we examine subclasses of LOGCFL arising from varying the arity and nesting of groupoidal quantifiers. Our work extends the elaborate theory relating monoidal quantifiers to NC1 and its subclasses. In the absence of the BIT predicate, we resolve the main issues: we show in particular that no single outermost unary groupoidal quantifier with FO can capture all the context-free languages, and we obtain the surprising result that a variant of Greibach's ``hardest context-free language'' is LOGCFL-complete under quantifier-free BIT-free projections. We then prove that FO with unary groupoidal quantifiers is strictly more expressive with the BIT predicate than without. Considering a particular groupoidal quantifier, we prove that first-order logic with majority of pairs is strictly more expressive than first-order with majority of individuals. As a technical tool of independent interest, we define the notion of an aperiodic nondeterministic finite automaton and prove that FO translations are precisely the mappings computed by single-valued aperiodic nondeterministic finite transducers.

cs.CC↗