95 research outputs found

    Eliminating Recursion from Monadic Datalog Programs on Trees

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    We study the problem of eliminating recursion from monadic datalog programs on trees with an infinite set of labels. We show that the boundedness problem, i.e., determining whether a datalog program is equivalent to some nonrecursive one is undecidable but the decidability is regained if the descendant relation is disallowed. Under similar restrictions we obtain decidability of the problem of equivalence to a given nonrecursive program. We investigate the connection between these two problems in more detail

    Pac-Learning Recursive Logic Programs: Efficient Algorithms

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    We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable. Two-clause programs consisting of one learnable recursive clause and one constant-depth determinate non-recursive clause are also learnable, if an additional ``basecase'' oracle is assumed. These results immediately imply the pac-learnability of these classes. Although these classes of learnable recursive programs are very constrained, it is shown in a companion paper that they are maximally general, in that generalizing either class in any natural way leads to a computationally difficult learning problem. Thus, taken together with its companion paper, this paper establishes a boundary of efficient learnability for recursive logic programs.Comment: See http://www.jair.org/ for any accompanying file

    Datalog extension for nested relations

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    AbstractThe nested relational model allows relations that are not in first normal form. This paper gives an extension of Datalog rules for nested relations. In our approach, nested Datalog is a natural extension of Datalog introduced for the relational data model. A nested Datalog program has a hierarchical structure of rules and subprograms to manipulate relation values of nested relations. We introduce a new category of predicate symbols, the variable predicate symbols to refer to tuples of subrelations. The notion of soundness, safety and consistency is defined to avoid undesirable nested Datalog programs. The evaluation of nested Datalog is given in terms of the nested relational algebra. Finally, we relate the expressive power of nonrecursive nested Datalog to the power of nested relational algebra and safe nested tuple relational calculus

    Stream Reasoning in Temporal Datalog

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    In recent years, there has been an increasing interest in extending traditional stream processing engines with logical, rule-based, reasoning capabilities. This poses significant theoretical and practical challenges since rules can derive new information and propagate it both towards past and future time points; as a result, streamed query answers can depend on data that has not yet been received, as well as on data that arrived far in the past. Stream reasoning algorithms, however, must be able to stream out query answers as soon as possible, and can only keep a limited number of previous input facts in memory. In this paper, we propose novel reasoning problems to deal with these challenges, and study their computational properties on Datalog extended with a temporal sort and the successor function (a core rule-based language for stream reasoning applications)

    Evaluating Datalog via Tree Automata and Cycluits

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    We investigate parameterizations of both database instances and queries that make query evaluation fixed-parameter tractable in combined complexity. We show that clique-frontier-guarded Datalog with stratified negation (CFG-Datalog) enjoys bilinear-time evaluation on structures of bounded treewidth for programs of bounded rule size. Such programs capture in particular conjunctive queries with simplicial decompositions of bounded width, guarded negation fragment queries of bounded CQ-rank, or two-way regular path queries. Our result is shown by translating to alternating two-way automata, whose semantics is defined via cyclic provenance circuits (cycluits) that can be tractably evaluated.Comment: 56 pages, 63 references. Journal version of "Combined Tractability of Query Evaluation via Tree Automata and Cycluits (Extended Version)" at arXiv:1612.04203. Up to the stylesheet, page/environment numbering, and possible minor publisher-induced changes, this is the exact content of the journal paper that will appear in Theory of Computing Systems. Update wrt version 1: latest reviewer feedbac

    Pac-learning Recursive Logic Programs: Negative Results

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    In a companion paper it was shown that the class of constant-depth determinate k-ary recursive clauses is efficiently learnable. In this paper we present negative results showing that any natural generalization of this class is hard to learn in Valiant's model of pac-learnability. In particular, we show that the following program classes are cryptographically hard to learn: programs with an unbounded number of constant-depth linear recursive clauses; programs with one constant-depth determinate clause containing an unbounded number of recursive calls; and programs with one linear recursive clause of constant locality. These results immediately imply the non-learnability of any more general class of programs. We also show that learning a constant-depth determinate program with either two linear recursive clauses or one linear recursive clause and one non-recursive clause is as hard as learning boolean DNF. Together with positive results from the companion paper, these negative results establish a boundary of efficient learnability for recursive function-free clauses.Comment: See http://www.jair.org/ for any accompanying file

    Regular Queries on Graph Databases

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    Graph databases are currently one of the most popular paradigms for storing data. One of the key conceptual differences between graph and relational databases is the focus on navigational queries that ask whether some nodes are connected by paths satisfying certain restrictions. This focus has driven the definition of several different query languages and the subsequent study of their fundamental properties. We define the graph query language of Regular Queries, which is a natural extension of unions of conjunctive 2-way regular path queries (UC2RPQs) and unions of conjunctive nested 2-way regular path queries (UCN2RPQs). Regular queries allow expressing complex regular patterns between nodes. We formalize regular queries as nonrecursive Datalog programs with transitive closure rules. This language has been previously considered, but its algorithmic properties are not well understood. Our main contribution is to show elementary tight bounds for the containment problem for regular queries. Specifically, we show that this problem is 2EXPSPACE-complete. For all extensions of regular queries known to date, the containment problem turns out to be non-elementary. Together with the fact that evaluating regular queries is not harder than evaluating UCN2RPQs, our results show that regular queries achieve a good balance between expressiveness and complexity, and constitute a well-behaved class that deserves further investigation

    Complexity and composition of synthesized web services

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    The paper investigates fundamental decision problems and composition synthesis for Web services commonly found in practice. We propose a notion of synthesized Web services (SWS’s) to specify the behaviors of the services. Upon receiving a sequence of input messages, an SWS issues multiple queries to a database and generates actions, in parallel; it produces external messages and database updates by synthesizing the actions parallelly generated. In contrast to previous models for Web services, SWS’s advocate parallel processing and (deterministic) synthesis of actions. We classify SWS’s based on what queries an SWS can issue, how the synthesis of actions is expressed, and whether unbounded input sequences are allowed in a single interaction session. We show that the behaviors of Web services supported by various prior models, data-driven or not, can be specified by different SWS classes. For each of these classes we study the non-emptiness, validation and equivalence problems, and establish matching upper and lower bounds on these problems. We also provide complexity bounds on composition synthesis for these SWS classes, identifying decidable cases
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