Jeffrey Considine | Searcharxiv

arXiv2024

Compressed Game Solving

We recast move generators for solving board games as operations on compressed sets of strings. We aim for compressed representations with space sublinear in the number of game positions for interesting sets of positions, move generation in time roughly linear in the compressed size and membership tests in constant time. To the extent that we achieve these tradeoffs empirically, we can strongly solve board games in time sublinear in the state space. We demonstrate this concept with the game Breakthrough where we empirically realize compressed representations taking roughly $n^{0.5}$ to $n^{0.7}$ space to store relevant sets of $n$ positions.

cs.DS↗

arXiv2003

Byzantine Agreement with Faulty Majority using Bounded Broadcast

Byzantine Agreement introduced in [Pease, Shostak, Lamport, 80] is a widely used building block of reliable distributed protocols. It simulates broadcast despite the presence of faulty parties within the network, traditionally using only private unicast links. Under such conditions, Byzantine Agreement requires more than 2/3 of the parties to be compliant. [Fitzi, Maurer, 00], constructed a Byzantine Agreement protocol for any compliant majority based on an additional primitive allowing transmission to any two parties simultaneously. They proposed a problem of generalizing these results to wider channels and fewer compliant parties. We prove that 2f < kh condition is necessary and sufficient for implementing broadcast with h compliant and f faulty parties using k-cast channels.

cs.DC↗