FA-72952 / Probabilistic sketches / Member archive

Counting Bloom filter with 4-bit counters: membership accepts partial matches · case 02

Items sharing only one counter with a stored item are reported present.

Member previewVariant 2 · 3 implementations · 9 checks per implementation

Case contract

Input {m, k, ops}; items are pre-hashed non-negative integers. Positions are the distinct values of (h1 + i*h2) mod m for i in 0..k-1 with h1 = item mod m and h2 = 1 + (item div m) mod (m-1), in first-seen order. add increments each distinct position once, saturating at 15. A saturated counter is sticky: remove never decrements it. remove is atomic: if any position is zero the result is "absent" and nothing changes; otherwise it decrements every non-saturated position. has requires every position to be positive. Return [results, counters].

Why this case matters

Counting Bloom filters support deletion in caches and routing tables; counter overflow, duplicate positions and non-atomic removals create false negatives that are otherwise impossible.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
duplicate probe positions	`[["added", "added", true, "removed", true, true], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]`	`[["added", "added", true, "removed", false, true], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]`	Failed

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