A separation logic for negative dependence

Formal reasoning about hashing-based probabilistic data structures often requires random variables where when one variable gets larger (such as the number of elements hashed into bucket), others tend to be smaller (like other buckets). This is an example negative dependence , a generalization independence that has recently found interesting applications in algorithm design and machine learning. Despite usefulness for analyses structures, existing verification methods cannot establish this property randomized programs. To fill gap, we LINA, separation logic dependence. Following recent works on using separating conjunction reason variables, use Our assertion features two conjunctions, We generalize bunched implications (BI) support multiple provide sound complete proof system. Notably, semantics relies non-deterministic rather than partial, operation combining resources. By drawing closure properties dependence, our program supports Frame-like rule monotone operations. demonstrate how LINA can verify hash-based balls-into-bins processes.