Causality, Knowledge and Coordination in Distributed Systems

Effecting coordination across remote sites in a distributed system is an essential part of distributed computing, and also an inherent challenge. In 1978, an analysis of communication in asynchronous systems was suggested by Leslie Lamport. Lamport's analysis determines a notion of temporal precedence, a sort of weak notion of time, which is otherwise missing in asynchronous systems. This notion has been extensively utilized in various applications. Yet the analysis is limited to systems that are asynchronous. In this thesis we go beyond by investigating causality in synchronous systems. In such systems, the boundaries of causal influence are not charted out exclusively by message passing. Here time itself, passing at a uniform (or almost uniform) rate for all processes, is also a medium by which causal influence may fan out. This thesis studies, and characterizes, the combinations of time and message passing that govern causal influence in synchronous systems. It turns out that knowledge based analysis [FHMV] provides a well tailored formal framework within which causal notions can be studied. As we show, the formal notion of knowledge is highly appropriate for characterizing causal influence in terms of information flow, broadening the analysis of Chandy and Misra in [ChM]. We define several generic classes of coordination problems that pose various temporal ordering requirements on the participating processes. These coordination problems provide natural generalizations of real life requirements. We then analyze the causal conditions that underlie suitable solutions to these problems. The analysis is conducted in two stages: first, the temporal ordering requirements are reduced to epistemic conditions. Then, these epistemic conditions are characterized in terms of the causal communication patterns that are necessary and sufficient to bring them about.Comment: PhD Dissertatio

A headache-causing problem

After disproving the celebrated Conway–Paterson–Moscow theorem [1], we prove that theorem and make an application to a well-known number-theoretic problem