Confluence Analysis for Distributed Programs: A Model-Theoretic Approach

Abstract

Building on recent interest in distributed logic programming, we take a model-theoretic approach to analyzing confluence of asynchronous distributed programs. We begin with a model-theoretic semantics for Dedalus and develop the concept of ultimate models to capture the non-deterministic eventual outcomes of distributed programs. After demonstrating the undecidability of checking confluence for Dedalus programs, we look for restricted sub-languages that guarantee confluence while providing adequate expressivity. We observe that a simple semipositive restriction called Dedalus + guarantees confluence while capturing PTIME, but demonstrate that the limited use of negation in Dedalus + makes certain simple and practical programs very difficult to express. To remedy this, we introduce Dedalus S , a restriction of Dedalus that allows a natural use of negation in the spirit of stratified negation, but retains the confluence of Dedalus + and similarly captures PTIME.

Deciding Confluence for a Simple Class of Relational Transducer Networks

“…For this reason, other approaches might be more viable, such as providing sufficient syntactic guarantees on consistency without unduly limiting the expressive power (e.g. [4,17]) and without imposing too much distributed coordination (e.g. [6,23]).…”

“…a z ) can be explained by a Turing machine transition applied to configuration i. 17 To send reach 0 (i, j), we have to check that such messages can be sent for all tape cells. We will simultaneously enforce that the state and head position of j can follow from the state and head position of i.…”

Lineage-driven Fault Injection

“…When the submitted Dedalus program is logically monotonic [5,58], LDFI answers how-to queries using positive why provenance [21]; otherwise LDFI must also consider the why-not provenance [40] of negated rule premises (e.g., "an acknowledgment was not received"). Systems such as Artemis [38] address the why-not problem (for monotonic queries) as a special case of what-if analysis, and ask what new (perhaps partially-specified) tuples would need to be added to a database to make a missing tuple appear.…”

Blazes: Coordination analysis for distributed programs

“…Ensuring consistent replica state by establishing a total order of message delivery is the technique adopted by state machine replication [30]; each component implements a deterministic state machine, and a global coordi- nation service such as atomic broadcast or Multipaxos decides the message order. Marczak et al draw a connection between stratified evaluation of conventional logic programming languages and distributed protocols to ensure consistency [39]. They describe a program rewrite that ensures deterministic executions by preventing any node from performing a nonmonotonic operation until that operation's inputs have stopped changing.…”