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.

We investigate the class D of queries that distribute over components. These are the queries that can be evaluated by taking the union of the query results over the connected components of the database instance. We show that it is undecidable whether a (positive) Datalog program distributes over components. Additionally, we show that connected Datalog¬ (the fragment of Datalog¬ where all rules are connected) provides an effective syntax for Datalog¬ programs that distribute over components under the stratified as well as under the well-founded semantics. As a corollary, we obtain a simple proof for one of the main results in previous work [Zinn et al. 2012], namely that the classic win-move query is in F 2 (a particular class of coordination-free queries).

The CALM-conjecture, first stated by Hellerstein [2010] and proved in its revised form by Ameloot et al. [2013] within the framework of relational transducer networks, asserts that a query has a coordination-free execution strategy if and only if the query is monotone. Zinn et al. [2012] extended the framework of relational transducer networks to allow for specific data distribution strategies and showed that the nonmonotone win-move query is coordination-free for domain-guided data distributions. In this article, we extend the story by equating increasingly larger classes of coordination-free computations with increasingly weaker forms of monotonicity and present explicit Datalog variants that capture each of these classes. One such fragment is based on stratified Datalog where rules are required to be connected with the exception of the last stratum. In addition, we characterize coordination-freeness as those computations that do not require knowledge about all other nodes in the network, and therefore, can not globally coordinate. The results in this article can be interpreted as a more fine-grained answer to the CALM-conjecture.

Abstract In the Declarative Networking paradigm, Datalog-like languages are used to express distributed computations. Whereas recently formal operational semantics for these languages have been developed, a corresponding declarative semantics has been lacking so far. The challenge is to capture precisely the amount of nondeterminism that is inherent to distributed computations due to concurrency, networking delays, and asynchronous communication. This paper shows how a declarative, model-based semantics can be obtained by simply using the well-known stable model semantics for Datalog with negation. We show that the model-based semantics matches previously proposed formal operational semantics.

We investigate the class D of queries that distribute over components. These are the queries that can be evaluated by taking the union of the query results over the connected components of the database instance. We show that it is undecidable whether a (positive) Datalog program distributes over components. Additionally, we show that connected Datalog with Negation (the fragment of Datalog with Negation where all rules are connected) provides an effective syntax for Datalog with Negation programs that distribute over components under the stratified as well as under the well-founded semantics. As a corollary, we obtain a simple proof for one of the main results in previous work [Zinn, Green, and Ludäscher, ICDT2012], namely, that the classic win-move query is in F_2 (a particular class of coordination-free queries).

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.

We study the expressive power of positive neural networks. The model uses positive connection weights and multiple input neurons. Different behaviors can be expressed by varying the connection weights. We show that in discrete time and in the absence of noise, the class of positive neural networks captures the so-called monotone-regular behaviors, which are based on regular languages. A finer picture emerges if one takes into account the delay by which a monotone-regular behavior is implemented. Each monotone-regular behavior can be implemented by a positive neural network with a delay of one time unit. Some monotone-regular behaviors can be implemented with zero delay. And, interestingly, some simple monotone-regular behaviors cannot be implemented with zero delay.

A distributed database system often operates in an asynchronous communication model where messages can be arbitrarily delayed. This communication model causes nondeterministic effects like unpredictable arrival orders of messages. Nonetheless, in general we want the distributed system to be deterministic; the system should produce the same output despite the nondeterministic effects on messages. Previously, two interpretations of determinism have been proposed. The first says that all infinite fair computation traces produce the same output. The second interpretation is a confluence notion, saying that all finite computation traces can still be extended to produce the same output. A decidability result for the confluence notion was previously obtained for so-called simple transducer networks, a model from the field of declarative networking. In the current article, we also present a decidability result for simple transducer networks, but this time for the first interpretation of determinism, with infinite fair computation traces. We also compare the expressivity of simple transducer networks under both interpretations.

Ensuring the correctness of a distributed system is an important challenge. Previously, two interpretations of correctness have been proposed: the first interpretation is about determinism, saying that all infinite fair computation traces produce the same output; and, the second interpretation is a confluence notion, saying that all finite computation traces can still be extended to produce the same output. A decidability result for the confluence notion was previously obtained for so-called simple transducer networks, a model from the field of declarative networking. In the current paper, we also present a decidability result for simple transducer networks, but this time for the first interpretation of correctness, with infinite fair computation traces. We also compare the expressivity of simple transducer networks under both interpretations.

The CALM-conjecture, first stated by Hellerstein [23] and proved in its revised form by Ameloot et al. [13] within the framework of relational transducer networks, asserts that a query has a coordination-free execution strategy if and only if the query is monotone. Zinn et al. [32] extended the framework of relational transducer networks to allow for specific data distribution strategies and showed that the nonmonotone win-move query is coordination-free for domain-guided data distributions. In this paper, we complete the story by equating increasingly larger classes of coordination-free computations with increasingly weaker forms of monotonicity and make Datalog variants explicit that capture each of these classes. One such fragment is based on stratified Datalog where rules are required to be connected with the exception of the last stratum. In addition, we characterize coordination-freeness as those computations that do not require knowledge about all other nodes in the network, and therefore, can not globally coordinate. The results in this paper can be interpreted as a more fine-grained answer to the CALM-conjecture.

The SQL standard offers three primitive operations (insert, delete, and update which is here called modify) to update a relation based on a generic query. This paper compares the expressiveness of programs composed of these three operations, with the general notion of update that simply replaces the content of the relation by the result of a query. It turns out that replacing cannot be expressed in terms of insertions, deletions, and modifications, and neither can modifications be expressed in terms of insertions and deletions. The expressive power gained by if-then-else control flow in programs is investigated as well. Different ways to perform replacing are discussed: using a temporary variable; using the new SQL merge operation; using SQL's data change delta tables; or using queries involving object creation or arithmetic. Finally the paper investigates the power of alternating the different primitives. For example, an insertion followed by a modification cannot always be expressed as a modification followed by an insertion.

Motivated by a recent conjecture concerning the expressiveness of declarative networking, we propose a formal computation model for “eventually consistent” distributed querying, based on relational transducers. A tight link has been conjectured between coordination-freeness of computations, and monotonicity of the queries expressed by such computations. Indeed, we propose a formal definition of coordination-freeness and confirm that the class of monotone queries is captured by coordination-free transducer networks. Coordination-freeness is a semantic property, but the syntactic class of “oblivious” transducers we define also captures the same class of monotone queries. Transducer networks that are not coordination-free are much more powerful.

Networks of relational transducers can serve as a formal model for declarative networking, focusing on distributed database querying applications. In declarative networking, a crucial property is eventual consistency, meaning that the final output does not depend on the message delays and re-orderings caused by the network. Here, we show that eventual consistency is decidable when the transducers satisfy some syntactic restrictions, some of which have also been considered in earlier work on automated verification of relational transducers. This simple class of transducer net-works computes exactly all distributed queries expressible by unions of conjunctive queries with negation.

Motivated by a recent conjecture concerning the expressiveness of declarative networking, we propose a formal computation model for "eventually consistent" distributed querying, based on relational transducers. A tight link has been conjectured between coordination-freeness of computations, and monotonicity of the queries expressed by such computations. Indeed, we propose a formal definition of coordination-freeness and confirm that the class of monotone queries is captured by coordination-free transducer networks. Coordination-freeness is a semantic property, but the syntactic class that we define of "oblivious" transducers also captures the same class of monotone queries. Transducer networks that are not coordination-free are much more powerful.