Confluence Analysis for Distributed Programs: A Model-Theoretic Approach

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 introduce the ultimate model, which captures non-deterministic eventual outcomes of distributed programs. After showing the question of confluence undecidable for Dedalus, we identify restricted sub-languages that guarantee confluence while providing adequate expressivity. We observe that the semipositive restriction Dedalus guarantees confluence while capturing PTIME, but show that its restriction of negation makes certain simple and practical programs difficult to write. To remedy this, we introduce DedalusS , a restriction of Dedalus that allows a kind of stratified negation, but retains the confluence of Dedalus and similarly captures PTIME.