<sc>D<inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="cai-ieq1-3124795.gif"/></alternatives></inline-formula>Abs</sc>: A Framework for Dynamic Dependence Analysis of Distributed 

As modern software systems are increasingly developed for running in distributed environments, it is crucial to provide fundamental techniques such as dependence analysis for checking, diagnosing, and evolving those systems. However, traditional dependence analysis is either inapplicable or of very limited utility for distributed programs due to the decoupled components of these programs which run in concurrent processes at physically separated machines. Motivated by the need for dependence analysis of distributed software and the diverse cost-effectiveness needs of dependence-based applications, this paper presents <sc>D<inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="cai-ieq2-3124795.gif"/></alternatives></inline-formula>Abs</sc>, a framework of dynamic dependence analysis for distributed programs. By partially ordering distributed method execution events and inferring causality from the ordered events, <sc>D<inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="cai-ieq3-3124795.gif"/></alternatives></inline-formula>Abs</sc> computes method-level dependencies both within and across process boundaries. Further, by exploiting message-passing semantics across processes, and incorporating static dependencies and statement coverage within individual components, <sc>D<inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="cai-ieq4-3124795.gif"/></alternatives></inline-formula>Abs</sc> offers three additional instantiations that trade efficiency for better precision. We present the design of the <sc>D<inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="cai-ieq5-3124795.gif"/></alternatives></inline-formula>Abs</sc> framework and evaluate the four instantiations of <sc>D<inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="cai-ieq6-3124795.gif"/></alternatives></inline-formula>Abs</sc> on distributed systems of various architectures and scales using our implementation for Java. Our empirical results show that <sc>D<inline-formula><tex-math notation="LaTeX">$^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow/><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href="cai-ieq7-3124795.gif"/></alternatives></inline-formula>Abs</sc> is significantly more effective than existing options while offering varying levels of cost-effectiveness tradeoffs. As our framework essentially computes whole-system run-time dependencies, it naturally empowers a range of other dependence-based applications.