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.

Consistency without borders

“…Certain components are insensitive to message delivery order-they produce a unique output set for all orderings and batchings of their inputs. We call such components confluent [48]. For example, the deadlock detector presented in Section 2 is confluent and can safely process waits-for edges as soon as they become available.…”

Logic and lattices for distributed programming

“…Intuitively, a monotonic program makes forward progress over time: it never "retracts" an earlier conclusion in the face of new information. We proposed the CALM theorem, which established that all monotonic programs are confluent (invariant to message reordering and retry) and hence eventually consistent [5,18,25]. Monotonicity of a Datalog program is straightforward to determine conservatively from syntax, so the CALM theorem provides the basis for a simple analysis of the consistency of distributed programs.…”

“…All monotonic programs are "eventually consistent" or confluent: for any given input, all program executions result in the same final state regardless of network non-determinism [5,25]. Hence, monotonic logic is a useful building block for loosely consistent distributed programming.…”

“…In recent work, we provided a modeltheoretic characterization of confluence for programs written in Dedalus, the formal language on which Bloom is based [25]. These results apply directly to Bloom, whose semantics are grounded in those of Dedalus.…”

Combining decidability paradigms for existential rules

“…In this context, the LP-based query language Datalog has been defined and intensively studied; see, e.g., (Ceri et al 1990). Interestingly, Datalog gone beyond its original purpose, and is now used in a variety of applications including web data extraction (Gottlob and Koch 2004), source code querying and program analysis (Hajiyev et al 2006), and distributed system analysis (Marczak et al 2012). Furthermore, since Datalog rules are clauses in the function-free Horn fragment of first-order logic, Datalog revealed itself relevant also for semantic web applications such as ontological modeling and reasoning.…”