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Confluence Analysis for Distributed Programs: A Model-Theoretic Approach

Marczak, William
Alvaro, Peter
Conway, Neil
Hellerstein, Joseph M.
Maier, David
Technical Report Identifier: EECS-2011-154
December 18, 2011

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.