What bloom filters do: probabilistically check set membership with no false negatives

How do Bloom filters utilize bit arrays to efficiently perform probabilistic set membership tests with minimal false positives?

Bloom filters use bit arrays to store hashed positions, allowing quick membership checks with controlled false positives

What consistent hashing does: minimizes remapping when nodes join/leave

Consistent hashing minimizes data redistribution during nodes' addition or removal

What database sharding does: splits data across machines by a partition key

Database sharding distributes data across multiple machines using a partition key for scalability and performance

What a sigma-algebra is: a collection of sets closed under complement and countable union

A sigma-algebra is a set of subsets closed under complementation and countable unions

Greedy vs beam search decoding: greedy picks best token, beam maintains k candidates

Greedy decoding selects one token, while beam search retains multiple candidates

What LSM trees optimize: write-heavy workloads by buffering writes in memory

LSM trees optimize write-heavy workloads through in-memory buffering