distributed system builders

Abstract: We study information aggregation in the networked learning model introduced by Kearns, Roth, and Ryu (SODA 2026). There is a fixed distribution over $d$ features and a common label. Agents learn in topological order on a directed acyclic graph. Each observes a subset of the features and its parents' predictions, fits a linear predictor to minimize mean squared error, and passes only its prediction forward. The global predictor is the best linear predictor using all features. Kearns, Roth, and Ryu show that the output agent's error approaches the global predictor's error along sufficiently deep paths with suitable feature coverage, while insufficient depth can prevent aggregation even in large networks. In contrast to their main focus on a given graph and feature allocation, we consider the limits of the model under two settings. In the adaptive designer setting, a designer chooses the graph, feature allocation, and output agent knowing the distribution. In the oblivious designer setting, the designer fixes all three before an adversary chooses the distribution. Each agent observes one feature and receives predictions from a limited number of parents. We call the aggregation exact when the output agent matches the global predictor exactly. For $d\ge3$, we show that no finite depth guarantees exact aggregation for every distribution with one parent per agent, even when the designer knows the distribution. In contrast, two parents per agent suffice for exact aggregation even in the oblivious designer setting. A fixed graph, feature allocation, and output agent achieve this for every distribution at depth $O(d\log d)$. Knowing the distribution reduces the depth to $O(d)$. Both constructions use $O(d^2)$ agents, with a very large constant for two parents. We show the bounds on the depth and number of agents are all optimal up to constant factors.

Abstract: This paper presents a precise executable specification---as a faithful mapping from the pseudocode---of Paxos for System Builders, a practical protocol for replication and consensus in distributed systems. Paxos for System Builders has both a robust implementation in C and a clean pseudocode for critical protocol details. This paper shows how the protocol pseudocode can be expressed easily, essentially line-by-line, in a precise high-level language, DistAlgo, for direct execution in distributed systems. Precise specification and direct execution help significantly in understanding the protocol logic and in automatically checking, tracing, and visualizing protocol runs. They also led to discoveries and fixes of small, difficult-to-catch omissions and liveness bugs in the pseudocode though not the C code. The resulting program also has acceptable performance while having similar size as the pseudocode.