Tom J. Ameloot

Relational transducers for declarative networking

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.

Deciding eventual consistency for a simple class of relational transducer networks

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.

Weaker forms of monotonicity for declarative networking: a more fine-grained answer to the calm-conjecture

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.

Parallel-Correctness and Transferability for Conjunctive 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.

On the CRON conjecture

Declarative networking is a recent approach to programming distributed applications with languages inspired by Datalog. A recent conjecture posits that the delivery of messages should respect causality if and only if they are used in non-monotone derivations. We present our results about this conjecture in the context of Dedalus, a Datalog-variant for distributed programming. We show that both directions of the conjecture fail under a strong semantical interpretation. But on a more syntactical level, we can show that positive Dedalus programs can tolerate non-causal messages, in the sense that they compute the correct answer when messages can be sent into the past.

Weaker Forms of Monotonicity for Declarative Networking: A More Fine-Grained Answer to the CALM-Conjecture

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.

Positive Dedalus programs tolerate non-causality

Abstract Declarative networking is a recent approach to programming distributed applications with languages inspired by Datalog. A recent conjecture posits that the delivery of messages should respect causality if and only if they are used in non-monotone derivations. We present our results about this conjecture in the context of Dedalus, a Datalog-variant for distributed programming. We show that both directions of the conjecture fail under a strong semantical interpretation. But on a more syntactical level, we show that positive Dedalus programs can tolerate non-causal messages, in the sense that they compute the correct answer even when messages can be sent into the past.

Data partitioning for single-round multi-join evaluation in massively parallel systems

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 provide a semantical characterization for when conjunctive queries (and extensions thereof) are parallel-correct and give matching complexity bounds for the associated decision problem. Motivated by scenarios for workload optimization, we further consider the problem of parallel-correctness transfer from a query Q to a query Q0, that is, whether Q0 is parallelcorrect for all distribution policies for which Q is parallelcorrect. In this case, Q0 can always be evaluated after Q without repartitioning the data. We provide a semantical characterization for parallel-correctness transfer and provide matching complexity bounds for the associated decision problem for conjunctive queries (and extensions). Finally, we investigate restrictions of queries and families of distribution policies with better complexities, including, for instance, the Hypercube distributions.

30 Years of PODS in facts and figures

We acknowledge the financial support of the Future and Emerging Technologies (FET) programme within the Seventh Framework Programme for Research of the European Commission, under the FET-Open grant agreement FOX, number FP7-ICT-233599.

Putting Logic-Based Distributed Systems on Stable Grounds

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.