The article studies query evaluation in parallel constant time in the CRCW PRAM model. While it is well-known that all relational algebra queries can be evaluated in constant time on an appropriate CRCW PRAM model, this article is interested in the efficiency of evaluation algorithms, that is, in the number of processors or, asymptotically equivalent, in the work. Naive evaluation in the parallel setting results in huge (polynomial) bounds on the work of such algorithms and in presentations of the result sets that can be extremely scattered in memory. The article discusses some obstacles for constant-time PRAM query evaluation. It presents algorithms for relational operators and explores three settings, in which efficient sequential query evaluation algorithms exist: acyclic queries, semijoin algebra queries, and join queries -- the latter in the worst-case optimal framework. Under mild assumptions -- that data values are numbers of polynomial size in the size of the database or that the relations of the database are suitably sorted -- constant-time algorithms are presented that are weakly work-efficient in the sense that work $\mathcal{O}(T^{1+\varepsilon})$ can be achieved, for every $\varepsilon>0$, compared to the time $T$ of an optimal sequential algorithm. Important tools are the algorithms for approximate prefix sums and compaction from Goldberg and Zwick (1995).

The paper proposes dynamic parallel algorithms for connectivity and bipartiteness of undirected graphs that require constant time and $O(n^{1/2+ε})$ work on the CRCW PRAM model. The work of these algorithms almost matches the work of the $O(\log n)$ time algorithm for connectivity by Kopelowitz et al. (2018) on the EREW PRAM model and the time of the sequential algorithm for bipartiteness by Eppstein et al. (1997). In particular, we show that the sparsification technique, which has been used in both mentioned papers, can in principle also be used for constant time algorithms in the CRCW PRAM model, despite the logarithmic depth of sparsification trees.

Previous work on Dynamic Complexity has established that there exist dynamic constant-time parallel algorithms for regular tree languages and context-free languages under label or symbol changes. However, these algorithms were not developed with the goal to minimise work (or, equivalently, the number of processors). In fact, their inspection yields the work bounds $O(n^2)$ and $O(n^7)$ per change operation, respectively. In this paper, dynamic algorithms for regular tree languages are proposed that generalise the previous algorithms in that they allow unbounded node rank and leaf insertions, while improving the work bound from $O(n^2)$ to $O(n^ε)$, for arbitrary $ε> 0$. For context-free languages, algorithms with better work bounds (compared with $O(n^7)$) for restricted classes are proposed: for every $ε> 0$ there are such algorithms for deterministic context-free languages with work bound $O(n^{3+ε})$ and for visibly pushdown languages with work bound $O(n^{2+ε})$.

The paper studies the rewriting problem, that is, the decision problem whether, for a given conjunctive query $Q$ and a set $\mathcal{V}$ of views, there is a conjunctive query $Q'$ over $\mathcal{V}$ that is equivalent to $Q$, for cases where the query, the views, and/or the desired rewriting are acyclic or even more restricted. It shows that, if $Q$ itself is acyclic, an acyclic rewriting exists if there is any rewriting. An analogous statement also holds for free-connex acyclic, hierarchical, and q-hierarchical queries. Regarding the complexity of the rewriting problem, the paper identifies a border between tractable and (presumably) intractable variants of the rewriting problem: for schemas of bounded arity, the acyclic rewriting problem is NP-hard, even if both $Q$ and the views in $\mathcal{V}$ are acyclic or hierarchical. However, it becomes tractable if the views are free-connex acyclic (i.e., in a nutshell, their body is (i) acyclic and (ii) remains acyclic if their head is added as an additional atom).

A short version will be presented at the conference FSTTCS 2022

The paper studies the rewriting problem, that is, the decision problem whether, for a given conjunctive query $Q$ and a set $\mathcal{V}$ of views, there is a conjunctive query $Q'$ over $\mathcal{V}$ that is equivalent to $Q$, for cases where the query, the views, and/or the desired rewriting are acyclic or even more restricted. It shows that, if $Q$ itself is acyclic, an acyclic rewriting exists if there is any rewriting. An analogous statement also holds for free-connex acyclic, hierarchical, and q-hierarchical queries. Regarding the complexity of the rewriting problem, the paper identifies a border between tractable and (presumably) intractable variants of the rewriting problem: for schemas of bounded arity, the acyclic rewriting problem is NP-hard, even if both $Q$ and the views in $\mathcal{V}$ are acyclic or hierarchical. However, it becomes tractable if the views are free-connex acyclic (i.e., in a nutshell, their body is (i) acyclic and (ii) remains acyclic if their head is added as an additional atom).

Abstract Which amount of parallel resources is needed for updating a query result after changing an input? In this work we study the amount of work required for dynamically answering membership and range queries for formal languages in parallel constant time with polynomially many processors. As a prerequisite, we propose a framework for specifying dynamic, parallel, constant-time programs that require small amounts of work. This framework is based on the dynamic descriptive complexity framework by Patnaik and Immerman.

The ACM PODS Alberto O. Mendelzon Test-of-Time Award is awarded every year to a paper or a small number of papers published in the PODS proceedings ten years prior that had the most impact in terms of research, methodology, or transfer to practice over the intervening decade. The PODS Executive Committee has appointed us to serve as the Award Committee for 2021. After careful consideration and having solicited external nominations and advice, we have selected the following paper as the award winner for 2021: Tight bounds for L_p samplers, finding duplicates in streams, and related problems by Hossein Jowhari, Mert Sağlam and Gábor Tardos Citation. This paper addresses a question posed by Cormode et al. in VLDB 2005, namely whether a uniform (or nearly uniform) sample can be maintained in a dynamically changing database, where data items may be inserted and deleted, while using space much smaller than the size of the database. More generally, it considers maintaining an L_p sample, where an element must be sampled with probability proportional to w^p (possibly up to some small relative error), where w is a weight that may change dynamically. In SODA 2010, Monemizadeh and Woodruff showed that it is possible to perform L_p sampling in a stream using polylogarithmic space. The PODS 2011 paper by Jowhari, Sağlam and Tardos essentially closes the problem by presenting algorithms with improved space usage, as well as a matching lower bound showing that it is not possible to asymptotically improve the upper bounds. The paper has had a considerable impact on the design of algorithms in streaming and distributed models of computation, where L_p sampling has become an essential part of the toolbox. The survey "L_p Samplers and Their Applications" in ACM Computing Surveys (2019) presents a number of surprising applications, for example in graph algorithms and in randomized numerical linear algebra.

Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic complexity class DynFO. This paper investigates extensions of DynFO in the spirit of parameterised algorithms. In this setting structures come with a parameter $k$ and the extensions allow additional "space" of size $f(k)$ (in the form of an additional structure of this size) or additional time $f(k)$ (in the form of iterations of formulas) or both. The resulting classes are compared with their non-dynamic counterparts and other classes. The main part of the paper explores the applicability of methods for parameterised algorithms to this setting through case studies for various well-known parameterised problems.

This paper introduces a declarative framework to specify and reason about distributions of data over computing nodes in a distributed setting. More specifically, it proposes distribution constraints which are tuple and equality generating dependencies (tgds and egds) extended with node variables ranging over computing nodes. In particular, they can express co-partitioning constraints and constraints about range-based data distributions by using comparison atoms. The main technical contribution is the study of the implication problem of distribution constraints. While implication is undecidable in general, relevant fragments of so-called data-full constraints are exhibited for which the corresponding implication problems are complete for EXPTIME, PSPACE and NP. These results yield bounds on deciding parallel-correctness for conjunctive queries in the presence of distribution constraints.

Recently, Ketsman et al. started the investigation of the parallel evaluation of recursive queries in the Massively Parallel Communication (MPC) model. Among other things, it was shown that parallel-correctness and parallel-boundedness for general Datalog programs is undecidable, by a reduction from the undecidable containment problem for Datalog. Furthermore, economic policies were introduced as a means to specify data distribution in a recursive setting. In this paper, we extend the latter framework to account for more general distributed evaluation strategies in terms of communication policies. We then show that the undecidability of parallel-correctness runs deeper: it already holds for fragments of Datalog, e.g., monadic and frontier-guarded Datalog, with a decidable containment problem, under relatively simple evaluation strategies. These simple evaluation strategies are defined w.r.t. data-moving distribution constraints. We then investigate restrictions of economic policies that yield decidability. In particular, we show that parallel-correctness is 2EXPTIME-complete for monadic and frontier-guarded Datalog under hash-based economic policies. Next, we consider restrictions of data-moving constraints and show that parallel-correctness and parallel-boundedness are 2EXPTIME-complete for frontier-guarded Datalog. Interestingly, distributed evaluation no longer preserves the usual containment relationships between fragments of Datalog. Indeed, not every monadic Datalog program is equivalent to a frontier-guarded one in the distributed setting. We illustrate the latter by considering two alternative settings where in one of these parallel-correctness is decidable for frontier-guarded Datalog but undecidable for monadic Datalog.

In the setting of DynFO, dynamic programs update the stored result of a query whenever the underlying data changes. This update is expressed in terms of first-order logic. We introduce a strategy for constructing dynamic programs that utilises periodic computation of auxiliary data from scratch and the ability to maintain a query for a limited number of change steps. We show that if some program can maintain a query for log n change steps after an AC$^1$-computable initialisation, it can be maintained by a first-order dynamic program as well, i.e., in DynFO. As an application, it is shown that decision and optimisation problems defined by monadic second-order (MSO) formulas are in DynFO, if only change sequences that produce graphs of bounded treewidth are allowed. To establish this result, a Feferman-Vaught-type composition theorem for MSO is established that might be useful in its own right.

Single-round multiway join algorithms first reshuffle data over many servers and then evaluate the query at hand in a parallel and communication-free way. A key question is whether a given distribution policy for the reshuffle is adequate for computing a given query, also referred to as parallel-correctness. This article extends the study of the complexity of parallel-correctness and its constituents, parallel-soundness and parallel-completeness, to unions of conjunctive queries with negation. As a by-product, it is shown that the containment problem for conjunctive queries with negation is coNEXPTIME-complete.

The Ackermann Award is the EACSL Outstanding Dissertation Award for Logic in Computer Science. It is presented during the annual conference of the EACSL (CSL'xx). This contribution reports on the 2018 edition of the award.

Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges. This article confirms their conjecture that the reachability query is in DynFO. As a byproduct, it is shown that the rank of a matrix with small values can be maintained in DynFO. It is further shown that the (size of the) maximum matching of a graph can be maintained in non-uniform DynFO, an extension of DynFO, with non-uniform initialisation of the auxiliary relations.

In the setting of dynamic complexity, the goal of a dynamic program is to maintain the result of a fixed query for an input database that is subject to changes, possibly using additional auxiliary relations. In other words, a dynamic program updates a materialized view whenever a base relation is changed. The update of query result and auxiliary relations is specified using first-order logic or, equivalently, relational algebra. The original framework by Patnaik and Immerman only considers changes to the database that insert or delete single tuples. This article extends the setting to definable changes , also specified by first-order queries on the database, and generalizes previous maintenance results to these more expressive change operations. More specifically, it is shown that the undirected reachability query is first-order maintainable under single-tuple changes and first-order defined insertions, likewise the directed reachability query for directed acyclic graphs is first-order maintainable under insertions defined by quantifier-free first-order queries. These results rely on bounded bridge properties , which basically say that, after an insertion of a defined set of edges, for each connected pair of nodes there is some path with a bounded number of new edges. While this bound can be huge, in general, it is shown to be small for insertion queries defined by unions of conjunctive queries. To illustrate that the results for this restricted setting could be practically relevant, they are complemented by an experimental study that compares the performance of dynamic programs with complex changes, dynamic programs with single changes, and with recomputation from scratch. The positive results are complemented by several inexpressibility results. For example, it is shown that—unlike for single-tuple insertions—dynamic programs that maintain the reachability query under definable, quantifier-free changes strictly need update formulas with quantifiers. Finally, further positive results unrelated to reachability are presented: it is shown that for changes definable by parameter-free first-order formulas, all LOGSPACE-definable (and even AC 1 -definable) queries can be maintained by first-order dynamic programs.

A strategy for constructing dynamic programs is introduced that utilises periodic computation of auxiliary data from scratch and the ability to maintain a query for a limited number of change steps. It is established that if some program can maintain a query for log n change steps after an AC^1-computable initialisation, it can be maintained by a first-order dynamic program as well, i.e., in DynFO. As an application, it is shown that decision and optimisation problems defined by monadic second-order (MSO) and guarded second-order logic (GSO) formulas are in DynFO, if only change sequences that produce graphs of bounded treewidth are allowed. To establish this result, Feferman-Vaught-type composition theorems for MSO and GSO are established that might be useful in their own right.

This paper studies dynamic complexity under definable change operations in the DynFO framework by Patnaik and Immerman. It is shown that for changes definable by parameter-free first-order formulas, all (uniform) AC1 queries can be maintained by first-order dynamic programs. Furthermore, many maintenance results for single-tuple changes are extended to more powerful change operations: (1) The reachability query for undirected graphs is first-order maintainable under single tuple changes and first-order defined insertions, likewise the reachability query for directed acyclic graphs under quantifier-free insertions. (2) Context-free languages are first-order maintainable under \EFO-defined changes. These results are complemented by several inexpressibility results, for example, that the reachability query cannot be maintained by quantifier-free programs under definable, quantifier-free deletions.

A dominant cost for query evaluation in modern massively distributed systems is the number of communication rounds. For this reason, there is a growing interest in single-round multiway join algorithms where data are first reshuffled over many servers and then evaluated in a parallel but communication-free way. The reshuffling itself is specified as a distribution policy. We introduce a correctness condition, called parallel-correctness , for the evaluation of queries w.r.t. a distribution policy. We study the complexity of parallel-correctness for conjunctive queries as well as transferability of parallel-correctness between queries. We also investigate the complexity of transferability for certain families of distribution policies, including the Hypercube distribution policies.

The article 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 article 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 article examines several extensions of active context-free games. The primary extension allows for 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 values returned by the services. In general, the complexity of the safe rewriting problem is highly intractable (doubly exponential time), but the article identifies relevant tractable cases.

While the migration from DTD to XML Schema was driven by a need for increased expressivity and flexibility, the latter was also significantly more complex to use and understand. Whereas DTDs are characterized by their simplicity, XML Schema Documents are notoriously difficult. In this article, we introduce the XML specification language BonXai, which incorporates many features of XML Schema but is arguably almost as easy to use as DTDs. In brief, the latter is achieved by sacrificing the explicit use of types in favor of simple patterns expressing contexts for elements. The goal of BonXai is not to replace XML Schema but rather to provide a simpler alternative for users who want to go beyond the expressiveness and features of DTD but do not need the explicit use of types. Furthermore, XML Schema processing tools can be used as a back-end for BonXai, since BonXai can be automatically converted into XML Schema. A particularly strong point of BonXai is its solid foundation rooted in a decade of theoretical work around pattern-based schemas. We present a formal model for a core fragment of BonXai and the translation algorithms to and from a core fragment of XML Schema. We prove that BonXai and XML Schema can be converted back-and-forth on the level of tree languages and we formally study the size trade-offs between the two languages.

Modern data management systems extensively use parallelism to speed up query processing over massive volumes of data. This trend has inspired a rich line of research on how to formally reason about the parallel complexity of join computation. In this paper, we go beyond joins and study the parallel evaluation of recursive queries. We introduce a novel framework to reason about multi-round evaluation of Datalog programs, which combines implicit predicate restriction with distribution policies to allow expressing a combination of data-parallel and query-parallel evaluation strategies. Using our framework, we reason about key properties of distributed Datalog evaluation, including parallel-correctness of the evaluation strategy, disjointness of the computation effort, and bounds on the number of communication rounds.

The goal of dynamic programs as introduced by Patnaik and Immerman (1994) is to maintain the result of a fixed query for an input database which is subject to tuple insertions and deletions. To this end such programs store an auxiliary database whose relations are updated via first-order formulas upon modifications of the input database. One of those auxiliary relations is supposed to store the answer to the query. Several static analysis problems can be associated to such dynamic programs. Is the answer relation of a given dynamic program always empty? Does a program actually maintain a query? That is, is the answer given of the program the same when an input database was reached by two different modification sequences? Even more, is the content of auxiliary relations independent of the modification sequence that lead to an input database? We study the algorithmic properties of those and similar static analysis problems. Since all these problems can easily be seen to be undecidable for full first-order programs, we examine the exact borderline for decidability for restricted programs. Our focus is on restricting the arity of the input databases as well as the auxiliary databases, and to restrict the use of quantifiers.

A dominant cost for query evaluation in modern massively distributed systems is the number of communication rounds. For this reason, there is a growing interest in single-round multiway join algorithms where data is first reshuffled over many servers and then evaluated in a parallel but communication-free way. The reshuffling itself is specified as a distribution policy. We introduce a correctness condition, called parallel-correctness, for the evaluation of queries w.r.t. a distribution policy. We study the complexity of parallel-correctness for conjunctive queries as well as transferability of parallel-correctness between queries. We also investigate the complexity of transferability for certain families of distribution policies, including, for instance, the Hypercube distribution.

While the migration from DTD to XML Schema was driven by a need for increased expressivity and flexibility, the latter was also significantly more complex to use and understand. Whereas DTDs are characterized by their simplicity, XML Schema Definitions (XSDs) are notoriously difficult. In this paper, we introduce the XML specification language BonXai which possesses most features of XSDs, including its expressivity, while retaining the simplicity of DTDs. In brief, the latter is achieved by sacrificing the explicit use of types in favor of simple patterns expressing contexts for elements. The goal of BonXai is by no means to replace XML Schema, but rather to provide a simpler DTD-like alternative to schema designers that do not need the explicit use of types. Therefore, BonXai can be seen as a practical front-end for XML Schema. A particular strong point of BonXai is its solid foundation rooted in a decade of theoretical work around pattern-based schemas. We present in detail the formal model for BonXai and discuss translation algorithms to and from XML Schema.

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.

BonXai is a versatile schema specification language expressively equivalent to XML Schema. It is not intended as a replacement for XML Schema but it can serve as an additional, user-friendly front-end. It offers a simple way and a lightweight syntax to specify the context of elements based on regular expressions rather than on types. In this demo we show the front-end capabilities of BonXai and exemplify its potential to offer a novel way to view existing XML Schema Definitions. In particular, we present several usage scenarios specifically targeted to showcase the ease of specifying, modifying, and understanding XML Schema Definitions through BonXai.

The article investigates the power of the dynamic complexity classes D yn FO, D yn QF, and D yn PROP 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 D yn PROP are exactly the regular languages, even when allowing arbitrary precomputation. This enables lower bounds for D yn PROP and separates D yn PROP from D yn QF and D yn FO. Further, it is shown that any context-free language can be maintained in D yn FO and a number of specific context-free languages, for example all Dyck-languages, are maintainable in D yn QF. 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 D yn PROP. On the other hand, any existential first-order property can be maintained in D yn QF when allowing precomputation.

The paper introduces key constraints for data words and shows that it is decidable whether, for a given two-variable sentence φ that can refer to the successor relation on positions and a set Κ of key constraints, there is a data string w that satisfies φ and respects Κ. Here, the formula is allowed to refer to the successor relation but not to the linear order on the positions of the word. As a byproduct, a self-contained exposition of an algorithm that decides satisfiability of such formulas (without key constraints) in 2-nexptime is given.

Frontmatter, Table of Contents, Preface, Conference Organization

In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. This model has been already considered in the realm of semistructured data, timed automata, and extended temporal logics. This article shows that satisfiability for the two-variable fragment FO 2 (∼,<,+1) of first-order logic with data equality test ∼ is decidable over finite and infinite data words. Here +1 and < are the usual successor and order predicates, respectively. The satisfiability problem is shown to be at least as hard as reachability in Petri nets. Several extensions of the logic are considered; some remain decidable while some are undecidable.

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.

Abiteboul et al. initiated the systematic study of distributed XML documents consisting of several logical parts, possibly located on different machines. The physical distribution of such documents immediately raises the following question: how can a global schema for the distributed document be broken up into local schemas for the different logical parts? The desired set of local schemas should guarantee that, if each logical part satisfies its local schema, then the distributed document satisfies the global schema.

The STACS conference of March 4-6, 2010, held in Nancy, is the 27th in this series. The STACS 2010 call for papers led to over 238 submissions from 40 countries. Each paper was assigned to three program committee members. The committee selected 54 papers during a two-week electronic meeting held in November.

Table of contents

We consider the problem of inferring a concise Document Type Definition (DTD) for a given set of XML-documents, a problem that basically reduces to learning concise regular expressions from positive examples strings. We identify two classes of concise regular expressions—the single occurrence regular expressions (SOREs) and the chain regular expressions (CHAREs)—that capture the far majority of expressions used in practical DTDs. For the inference of SOREs we present several algorithms that first infer an automaton for a given set of example strings and then translate that automaton to a corresponding SORE, possibly repairing the automaton when no equivalent SORE can be found. In the process, we introduce a novel automaton to regular expression rewrite technique which is of independent interest. When only a very small amount of XML data is available, however (for instance when the data is generated by Web service requests or by answers to queries), these algorithms produce regular expressions that are too specific. Therefore, we introduce a novel learning algorithm crx that directly infers CHAREs (which form a subclass of SOREs) without going through an automaton representation. We show that crx performs very well within its target class on very small datasets.

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.

Motivated by reasoning tasks for XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result, decidability of satisfiability and containment for a data-aware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.

The generalized hypertree width GHW( H ) of a hypergraph H is a measure of its cyclicity. Classes of conjunctive queries or constraint satisfaction problems whose associated hypergraphs have bounded GHW are known to be solvable in polynomial time. However, it has been an open problem for several years if for a fixed constant k and input hypergraph H it can be determined in polynomial time whether GHW( H ) ≤ k . Here, this problem is settled by proving that even for k = 3 the problem is already NP-hard. On the way to this result, another long standing open problem, originally raised by Goodman and Shmueli [1984] in the context of join optimization is solved. It is proven that determining whether a hypergraph H admits a tree projection with respect to a hypergraph G is NP-complete. Our intractability results on generalized hypertree width motivate further research on more restrictive tractable hypergraph decomposition methods that approximate generalized hypertree decomposition (GHD). We show that each such method is dominated by a tractable decomposition method definable through a function that associates a set of partial edges to a hypergraph. By using one particular such function, we define the new Component Hypertree Decomposition method, which is tractable and strictly more general than other approximations to GHD published so far.

We study the complexity of the inclusion, equivalence, and intersection problem of extended chain regular expressions (eCHAREs). These are regular expressions with a very simple structure: they basically consist of the concatenation of factors, where each factor is a disjunction of strings, possibly extended with “$*$”, “$+$”, or “$?$”. Though of a very simple form, the usage of such expressions is widespread as eCHAREs, for instance, constitute a super class of the regular expressions most frequently used in practice in schema languages for XML. In particular, we show that all our lower and upper bounds for the inclusion and equivalence problem carry over to the corresponding decision problems for extended context-free grammars, and to single-type and restrained competition tree grammars. These grammars form abstractions of document type definitions (DTDs), XML schema definitions (XSDs) and the class of one-pass preorder typeable XML Schemas, respectively. For the intersection problem, we show that obtained complexities only carry over to DTDs. In this respect, we also study two other classes of regular expressions related to XML: deterministic expressions and expressions where the number of occurrences of alphabet symbols is bounded by a constant.

Finite or infinite strings or trees with labels from a finite alphabet play an important role in computer science. They can be used to model many interesting objects including system runs in Automated Verification and XML documents in Database Theory. They allow the application of formal tools like logical formulas to specify properties and automata for their implementation. In this framework, many reasoning tasks that are undecidable for general computational models can be solved algorithmically, sometimes even efficiently. Nevertheless, the use of finitely labelled structures usually requires an early abstraction from the real data. For example, theoretical research on XML processing very often con- centrates on the document structure (including labels) but ignores attribute or text values. While this abstraction has led to many interesting results, some aspects like key or other integrity constraints can not be adequately handled. In Automated Verification of software systems or communication protocols, infinite domains occur even more naturally, e.g., induced by program data, recursion, time, com- munication or by unbounded numbers of concurrent processes. Usually one approximates infinite domains by finite ones in a very early abstraction step. An alternative approach that has been investigated in recent years is to extend strings and trees by (a limited amount of) data and to use logical languages with a restricted ex- pressive power concerning this data. As an example, in the most simple setting, formulas can only test equality of data values. The driving goal is to identify logical languages and corresponding automata models which are strong enough to describe interesting proper- ties of data-enhanced structures while keeping decidability or even feasibility of automatic reasoning. The talk gives a basic introduction into data-enhanced finitely labelled structures, presents examples of their use, and highlights recent decidability and complexity results.

No abstract available.

The generalized hypertree width GHW(H) of a hypergraph H is a measure of its cyclicity. Classes of conjunctive queries or constraint satisfaction problems whose associated hypergraphs have bounded GHW are known to be solvable in polynomial time. However,it has been an open problem for several years if for a fixed constant k and input hypergraph H it can be determined in polynomial time whether GHW(H)< k. Here, this problem is settled by proving that even for k=3 the problem is already NP-hard. On the way to this result, another long standing open problem, originally raised by Goodman and Shmueli in 1984 all in the context of join optimization is solved. It is proven that determining whether a hypergraph H admits a tree projection with respect to a hypergraph G is NP-complete. Our intractability results on generalized hypertree width motivate further research on more restrictive tractable hypergraph decomposition methods that approximate general hypertree decomposition (GHD). We show that each such method is dnominated by a tractable decomposition method definable through a function that associates a set of partial edges to a hypergraph. By using one particular such function, we define the new Component Hypertree Decomposition method, which is tractable and strictly more general than other approximations to GHD published so far.

In a recent paper, Martens et al. introduced a specification mechanism for XML tree languages, based on rules of the form (r,s), wherer, s are regular expressions. Sets of such rules can be interpreted in an existential or a universal fashion. An XML tree is existentially valid with respect to a rule set, if for each node there is a rule such that the root path of the node matches r and the children sequence of the node matchess. It is universally valid if each node matching r also matchess. This paper investigates the complexity of reasoning about such rule sets, in particular the satisfiability and the implication problem. Whereas, in general these reasoning problems are complete for EXPTIME, two important fragments are identified with PSPACE and PTIME complexity, respectively.

In a data word each position carries a label from a finite alphabet and a data value from some infinite domain. These models have been already considered in the realm of semistructured data, timed automata and extended temporal logics. It is shown that satisfiability for the two-variable first-order logic FO^2(~,\le,+1) is decidable over finite and over infinite data words, where ¡« is a binary predicate testing the data value equality and +1,\le are the usual successor and order predicates. The complexity of the problem is at least as hard as Petri net reachability. Several extensions of the logic are considered, some remain decidable while some are undecidable.

Motivated by reasoning tasks in the context of XML languages, the satisfiability problem of logics on data trees is investigated. The nodes of a data tree have a label from a finite set and a data value from a possibly infinite set. It is shown that satisfiability for two-variable first-order logic is decidable if the tree structure can be accessed only through the child and the next sibling predicates and the access to data values is restricted to equality tests. From this main result decidability of satisfiability and containment for a data-aware fragment of XPath and of the implication problem for unary key and inclusion constraints is concluded.

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.

The common abstraction of XML Schema by unranked regular tree languages is not entirely accurate. To shed some light on the actual expressive power of XML Schema, intuitive semantical characterizations of the Element Declarations Consistent (EDC) rule are provided. In particular, it is obtained that schemas satisfying EDC can only reason about regular properties of ancestors of nodes. Hence, with respect to expressive power, XML Schema is closer to DTDs than to tree automata. These theoretical results are complemented with an investigation of the XML Schema Definitions (XSDs) occurring in practice, revealing that the extra expressiveness of XSDs over DTDs is only used to a very limited extent. As this might be due to the complexity of the XML Schema specification and the difficulty of understanding the effect of constraints on typing and validation of schemas, a simpler formalism equivalent to XSDs is proposed. It is based on contextual patterns rather than on recursive types and it might serve as a light-weight front end for XML Schema. Next, the effect of EDC on the way XML documents can be typed is discussed. It is argued that a cleaner, more robust, larger but equally feasible class is obtained by replacing EDC with the notion of 1-pass preorder typing (1PPT): schemas that allow one to determine the type of an element of a streaming document when its opening tag is met. This notion can be defined in terms of grammars with restrained competition regular expressions and there is again an equivalent syntactical formalism based on contextual patterns. Finally, algorithms for recognition, simplification, and inclusion of schemas for the various classes are given.

On an abstract level, XML Schema increases the limited expressive power of Document Type Definitions (DTDs) by extending them with a recursive typing mechanism. However, an investigation of the XML Schema Definitions (XSDs) occurring in practice reveals that the vast majority of them are structurally equivalent to DTDs. This might be due to the complexity of the XML Schema specification and the difficulty to understand the effect of constraints on typing and validation of schemas. To shed some light on the actual expressive power of XSDs this paper studies the impact of the Element Declarations Consistent (EDC) and the Unique Particle Attribution (UPA) rule. An equivalent formalism based on contextual patterns rather than on recursive types is proposed which might serve as a light-weight front end for XML Schema. Finally, the effect of EDC and UPA on the way XML documents can be typed is discussed. It is argued that a cleaner, more robust, stronger but equally efficient class is obtained by replacing EDC and UPA with the notion of 1-pass preorder typing: schemas that allow to determine the type of an element of a streaming document when its opening tag is met. This notion can be defined in terms of restrained competition regular expressions and there is again an equivalent syntactical formalism based on contextual patterns.

Formal languages play an important role for many aspects of XML processing. This is obvious for type specifications (as DTD) which use context-free grammars and for navigation in documents (as in XPath) which is based on regular expressions. But the investigation of query, typing, navigation and transformation languages for XML has used many more concepts from Formal Language Theory, in particular many different kinds of string and tree automata.The close connection between automata and logics helps to allow a declarative specification of queries and transformations that can be evaluated or performed by tree automata. This connection also facilitates the investigation of the expressive power of query and transformation languages. Furthermore, in many cases automata characterizations enable static analysis like containment and satisfiability tests for queries or type checking for transformations.The tutorial will give a gentle introduction into the connections between XML languages and various kinds of automata and it will survey some classical and recent results in this area.

Fagin's theorem, the first important result of descriptive complexity, asserts that a property of graphs is in NP if and only if it is definable by an existential second-order formula. In this article, we study the complexity of evaluating existential second-order formulas that belong to prefix classses of existential second-order logic, where a prefix class is the collection of all existential second-order formulas in prenex normal form such that the second-order and the first-order quantifiers obey a certain quantifier pattern. We completely characterize the computational complexity of prefix classes of existential second-order logic in three different contexts: (1) over directed graphs, (2) over undirected graphs with self-loops and (3) over undirected graphs without self-loops. Our main result is that in each of these three contexts a dichotomy holds, that is to say, each prefix class of existential second-order logic either contains sentences that can express NP-complete problems, or each of its sentences expresses a polynomial-time solvable problem. Although the boundary of the dichotomy coincides for the first two cases, it changes, as one moves to undirected graphs without self-loops. The key difference is that a certain prefix class, based on the well-known Ackermann class of first-order logic, contains sentences that can express NP-complete problems over graphs of the first two types, but becomes tractable over undirected graphs without self-loops. Moreover, establishing the dichotomy over undirected graphs without self-loops turns out to be a technically challenging problem that requires the use of sophisticated machinery from graph theory and combinatorics, including results about graphs of bounded tree-width and Ramsey's theorem.

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 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.

Motivated by formal models recently proposed in the context of XML, we study automata and logics on strings over infinite alphabets. These are conservative extensions of classical automata and logics defining the regular languages on finite alphabets. Specifically, we consider register and pebble automata, and extensions of first-order logic and monadic second-order logic. For each type of automaton we consider one-way and two-way variants, as well as deterministic, nondeterministic, and alternating control. We investigate the expressiveness and complexity of the automata and their connection to the logics, as well as standard decision problems. Some of our results answer open questions of Kaminski and Francez on register automata.

A query against a database behind a site like Napster may search, e.g., for all users who have downloaded more jazz titles than pop music titles. In order to express such queries, we extend classical monadic second-order logic by Presburger predicates which pose numerical restrictions on the children (content) of an element node and provide a precise automata-theoretic characterization. While the existential fragment of the resulting logic is decidable, it turns out that satisfiability of the full logic is undecidable. Decidable satisfiability and a querying algorithm even with linear data complexity can be obtained if numerical constraints are only applied to those contents of elements where ordering is irrelevant. Finally, it is sketched how these techniques can be extended also to answer questions like, e.g., whether the total price of the jazz music downloaded so far exceeds a user's budget.

We study analogs of classical relational calculus in the context of strings. We start by studying string logics. Taking a classical model-theoretic approach, we fix a set of string operations and look at the resulting collection of definable relations. These form an algebra---a class ofn-ary relations for everyn, closed under projection and Boolean operations. We show that by choosing the string vocabulary carefully, we get string logics that have desirable properties: computable evaluation and normal forms. We identify five distinct models and study the differences in their model-theory and complexity of evaluation. We identify a subset of these models that have additional attractive properties, such as finite VC dimension and quantifier elimination.Once you have a logic, the addition of free predicate symbols gives you a string query language. The resulting languages have attractive closure properties from a database point of view: while SQL does not allow the full composition of string pattern-matching expressions with relational operators, these logics yield compositional query languages that can capture common string-matching queries while remaining tractable. For each of the logics studied in the first part of the article, we study properties of the corresponding query languages. We give bounds on the data complexity of queries, extend the normal form results from logics to queries, and show that the languages have corresponding algebras expressing safe queries.

This article presents two algebraic characterizations and two related complete problems for the complexity class DLIN that was introduced in [E. Grandjean, Ann. Math. Artif. Intell., 16 (1996), pp. 183--236]. DLIN is essentially the class of all functions that can be computed in linear time on a Random Access Machine which uses only numbers of linear value during its computations. The algebraic characterizations are in terms of recursion schemes that define unary functions. One of these schemes defines several functions simultaneously, while the other one defines only one function. From the algebraic characterizations, we derive two complete problems for DLIN under new, very strict, and machine-independent affine reductions.

We study algebras of definable string relations, classes of regular n-ary relations that arise as the definable sets within a model whose carrier is the set of all strings. We show that the largest such algebra-the collection of regular relations-has some quite undesirable computational and model-theoretic properties. In contrast, we exhibit several definable relation algebras that have much tamer behavior: for example, they admit quantifier elimination, and have finite VC dimension. We show that the properties of a definable relation algebra are not at all determined by the one-dimensional definable sets. We give models whose definable sets are all star-free, but whose binary relations are quite complex, as well as models whose definable sets include all regular sets, but which are much more restricted and tractable than the full algebra of regular relations.

We study relational calculi with support for string operations. While SQL restricts the ability to mix string pattern-matching and relational operations, prior proposals for embedding SQL in a compositional calculus were based on adding the operation of concatenation to first-order logic. These latter proposals yield compositional query languages extending SQL, but are unfortunately computationally complete. The unbounded expressive power in turn implies strong limits on the ability to perform optimization and static analysis of properties such as query safety in these languages.

The evaluation of conjunctive queries is hard both with respect to its combined complexity (NP-complete) and its parameterized complexity (W[1]-complete). It becomes tractable (PTIME for combined complexity, FPT for parameterized complexity), when the underlying graphs of the conjunctive queries have bounded tree-width [2]. We show that, in some sense, this is optimal both with respect to combined and parameterized complexity: For every class C of graphs, the evaluation of all conjunctive queries whose underlying graph is in C is tractable if, and only if, C has bounded tree-width.

Fagin's (1974) theorem, the first important result of descriptive complexity, asserts that a property of graphs is in NP if and only if it is definable by an existential second-order formula. We study the complexity of evaluating existential second-order formulas that belong to prefix classes of existential second-order logic, where a prefix class is the collection of all existential second-order and the first-order quantifiers obey a certain quantifier pattern. We completely characterize the computation complexity of prefix classes of existential second-order logic in three different contexts: over directed graphs; over undirected graphs with self-loops; and over undirected graphs without self-loops. Our main result is that in each of these three contexts a dichotomy holds, i.e., each prefix class of existential second-order logic either contains sentences that can express NP-complete problems or each of its sentences expresses a polynomial-time solvable problem. Although the boundary of the dichotomy coincides for the first two cases, it changes, as one move to undirected graphs without self-loops.

It would be desirable to have a query language for tree-structured data that is (1) as easily usable as SQL, (2) as expressive as monadic second-order logic (MSO), and (3) efficiently evaluable. The paper develops some ideas in this direction. Towards (1) the specification of sets of vertices of a tree by combining conditions on their induced subtree with conditions on their path to the root is proposed. Existing query languages allow regular expressions (hence MSO logic) in path conditions but are limited in expressing subtree conditions. It is shown that such query languages fall short of capturing all MSO queries. On the other hand, allowing a certain guarded fragment of MSO-logic in the specification of subtree conditions results in a language fulfilling (2), (3) and, anguably, (1).

A query is local if the decision of whether a tuple in a structure satisfies this query only depends on a small neighborhood of the tuple. We prove that all queries expressible by order-invariant first-order formulas are local.

It is common to model structured document databases by context-free and extended context-free grammars.A crucial difference is that the derivation trees of the former are ranked, while those of the latter are not.A main task in document transformation and information retrieval is locating subtrees satisfying some pattern.Therefore, unary queries, i.e., queries that map a tree to a set of its nodes, play an important role in the context of structured document databases.We want to understand how the natural and well-studied computation model of tree automata can be used to express such queries.We define a query automaton (QA) as a deterministic two-way finite automaton over trees that has the ability to select nodes depending on the state and the label at those nodes.We study QAs over ranked as well as over unranked trees.More precisely, we characterize the expressiveness of the different formalisms by linking them to monadic second-order logic, and we establish the complexity of their non-emptiness and equivalence problem.

Binary NP consists of all sets of finite structures which are expressible in existential second-order logic with second-order quantification restricted to relations of arity 2. We look at semantical restrictions of binary NP, where the second order quantifiers range only over certain classes of relations. We consider mainly three types of classes of relations: unary functions, order relations and graphs with degree bounds. We show that many of these restrictions have the same expressive power and establish a four-level strict hierarchy, represented by sets, permutations, unary functions and arbitrary binary relations, respectively.

Continuing a line of research opened up by Grigni and Sipser (1992) and further pursued by Stewart (1994), we show that a wide variety of equivalent characterizations of P still remain equivalent when restricted to be positive. All these restrictions thus define the same class posP, a proper subclass of monP, the class of monotone problems in P. We also exhibit complete problems for posP under very weak reductions.

Ehrenfeucht games are a useful tool in proving that certain properties of finite structures are not expressible by formulas of a certain type. In this paper a new method is introduced that allows the extension of a local winning strategy for Duplicator, one of the two players in Ehrenfeucht games, to a global winning strategy. As an application it is shown that graph connectivity cannot be expressed by existential second-order formulas, where the second-order quantification is restricted to unary relations (monadic NP), even, in the presence of a built-in linear order. As a second application it is stated, that, on the other hand, the presence of a linear order increases the power of monadic NP more than the presence of a successor relation.>