FA-72931 / Probabilistic sketches / Open access
Counting Bloom filter with 4-bit counters: stride can be congruent to zero · case 01
Some items probe a single counter k times, raising their false-positive and false-negative exposure.
ROOT CAUSE
The stride is taken modulo m without the +1 offset, so a zero stride is possible.
THE FAILURE
The stride is taken modulo m without the +1 offset, so a zero stride is possible.
Unsuccessful approach: Adding one after reducing modulo m still yields a stride equal to m, which is again congruent to zero.
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.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
m = x['m']
k = x['k']
c = [0] * m
def positions(item):
h1 = item % m
h2 = (item // m) % m
out = []
for i in range(k):
p = (h1 + i * h2) % m
if p not in out:
out.append(p)
return out
res = []
for op, item in x['ops']:
pos = positions(item)
if op == 'add':
for p in pos:
if c[p] < 15:
c[p] = c[p] + 1
res.append('added')
elif op == 'remove':
if any(c[p] == 0 for p in pos):
res.append('absent')
continue
for p in pos:
if c[p] < 15:
c[p] = c[p] - 1
res.append('removed')
else:
res.append(all(c[p] > 0 for p in pos))
return [res, c]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['duplicate probe positions',
{'k': 4,
'm': 12,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 12,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 12, 'ops': [['add', 137], ['add', 8], ['has', 137], ['remove', 8]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 12,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 12, 'ops': [['add', 6], ['remove', 42], ['has', 6]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 12, 'ops': [['add', 2], ['add', 14], ['has', 26], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 12, 'ops': [['add', 31], ['add', 32], ['remove', 31], ['has', 31], ['has', 32]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]]],
['remove absent from empty',
{'k': 2, 'm': 12, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 12,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 14,
'ops': [['add', 87], ['add', 1], ['has', 87], ['remove', 87], ['has', 87], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 14,
'ops': [['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['has', 87]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 14, 'ops': [['add', 187], ['add', 9], ['has', 187], ['remove', 9]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 14,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 14, 'ops': [['add', 7], ['remove', 49], ['has', 7]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 14, 'ops': [['add', 2], ['add', 16], ['has', 30], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 14, 'ops': [['add', 32], ['add', 33], ['remove', 32], ['has', 32], ['has', 33]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 14, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 14,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 15,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 15,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 15, 'ops': [['add', 215], ['add', 10], ['has', 215], ['remove', 10]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 15,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 15, 'ops': [['add', 8], ['remove', 53], ['has', 8]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 15, 'ops': [['add', 2], ['add', 17], ['has', 32], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 15, 'ops': [['add', 33], ['add', 34], ['remove', 33], ['has', 33], ['has', 34]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 15, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 15,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 16,
'ops': [['add', 115], ['add', 1], ['has', 115], ['remove', 115], ['has', 115], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 16,
'ops': [['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['has', 115]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 16, 'ops': [['add', 245], ['add', 11], ['has', 245], ['remove', 11]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 16,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 16, 'ops': [['add', 9], ['remove', 57], ['has', 9]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 16, 'ops': [['add', 2], ['add', 18], ['has', 34], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 16, 'ops': [['add', 34], ['add', 35], ['remove', 34], ['has', 34], ['has', 35]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 16, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 16,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 18,
'ops': [['add', 147], ['add', 1], ['has', 147], ['remove', 147], ['has', 147], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 18,
'ops': [['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['has', 147]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 18, 'ops': [['add', 311], ['add', 12], ['has', 311], ['remove', 12]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 18,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 18, 'ops': [['add', 10], ['remove', 64], ['has', 10]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 18, 'ops': [['add', 2], ['add', 20], ['has', 38], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True],
[0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 18, 'ops': [['add', 35], ['add', 36], ['remove', 35], ['has', 35], ['has', 36]]},
[['added', 'added', 'removed', False, True],
[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 18, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 18,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]]]
for label, args, expected in cases[N - 1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| duplicate probe positions | [['added', 'added', True, 'removed', False, True], [0, 1, 0, 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]] | Failed |
| hot item with repeated positions | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| wide stride item | [['added', 'added', True, 'removed'], [0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]] | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] | Failed |
| saturating counter | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]] | Failed |
| atomic removal of absent item | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0]] | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | Failed |
| partial overlap membership | [['added', 'added', False, True, True], [0, 0, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | Failed |
| normal add and remove | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0]] | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | Failed |
| remove absent from empty | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| saturated then drained | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', True], [0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', True], [0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]] | Passed |
SHA-256 / f4adf04fb64259a97fc065e87912a0d1e544749b2dc0f6c780d7853622f11605
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
m = x['m']
k = x['k']
c = [0] * m
def positions(item):
h1 = item % m
h2 = 1 + (item // m) % m
out = []
for i in range(k):
p = (h1 + i * h2) % m
if p not in out:
out.append(p)
return out
res = []
for op, item in x['ops']:
pos = positions(item)
if op == 'add':
for p in pos:
if c[p] < 15:
c[p] = c[p] + 1
res.append('added')
elif op == 'remove':
if any(c[p] == 0 for p in pos):
res.append('absent')
continue
for p in pos:
if c[p] < 15:
c[p] = c[p] - 1
res.append('removed')
else:
res.append(all(c[p] > 0 for p in pos))
return [res, c]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['duplicate probe positions',
{'k': 4,
'm': 12,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 12,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 12, 'ops': [['add', 137], ['add', 8], ['has', 137], ['remove', 8]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 12,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 12, 'ops': [['add', 6], ['remove', 42], ['has', 6]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 12, 'ops': [['add', 2], ['add', 14], ['has', 26], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 12, 'ops': [['add', 31], ['add', 32], ['remove', 31], ['has', 31], ['has', 32]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]]],
['remove absent from empty',
{'k': 2, 'm': 12, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 12,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 14,
'ops': [['add', 87], ['add', 1], ['has', 87], ['remove', 87], ['has', 87], ['has', 1]]},
[['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 14,
'ops': [['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['add', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['remove', 87],
['has', 87]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 14, 'ops': [['add', 187], ['add', 9], ['has', 187], ['remove', 9]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 14,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 14, 'ops': [['add', 7], ['remove', 49], ['has', 7]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 14, 'ops': [['add', 2], ['add', 16], ['has', 30], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 14, 'ops': [['add', 32], ['add', 33], ['remove', 32], ['has', 32], ['has', 33]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 14, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 14,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 15,
'ops': [['add', 63], ['add', 1], ['has', 63], ['remove', 63], ['has', 63], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 15,
'ops': [['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['add', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['remove', 63],
['has', 63]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 15, 'ops': [['add', 215], ['add', 10], ['has', 215], ['remove', 10]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 15,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 15, 'ops': [['add', 8], ['remove', 53], ['has', 8]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 15, 'ops': [['add', 2], ['add', 17], ['has', 32], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 15, 'ops': [['add', 33], ['add', 34], ['remove', 33], ['has', 33], ['has', 34]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 15, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 15,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 16,
'ops': [['add', 115], ['add', 1], ['has', 115], ['remove', 115], ['has', 115], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 16,
'ops': [['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['add', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['remove', 115],
['has', 115]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 16, 'ops': [['add', 245], ['add', 11], ['has', 245], ['remove', 11]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 16,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 16, 'ops': [['add', 9], ['remove', 57], ['has', 9]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 16, 'ops': [['add', 2], ['add', 18], ['has', 34], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 16, 'ops': [['add', 34], ['add', 35], ['remove', 34], ['has', 34], ['has', 35]]},
[['added', 'added', 'removed', False, True], [0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 16, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 16,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]],
[['duplicate probe positions',
{'k': 4,
'm': 18,
'ops': [['add', 147], ['add', 1], ['has', 147], ['remove', 147], ['has', 147], ['has', 1]]},
[['added', 'added', True, 'removed', False, True],
[0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['hot item with repeated positions',
{'k': 4,
'm': 18,
'ops': [['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['add', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['remove', 147],
['has', 147]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
False],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['wide stride item',
{'k': 3, 'm': 18, 'ops': [['add', 311], ['add', 12], ['has', 311], ['remove', 12]]},
[['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturating counter',
{'k': 2,
'm': 18,
'ops': [['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['add', 4],
['remove', 4],
['has', 4]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
True],
[0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['atomic removal of absent item',
{'k': 3, 'm': 18, 'ops': [['add', 10], ['remove', 64], ['has', 10]]},
[['added', 'absent', True], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0]]],
['partial overlap membership',
{'k': 3, 'm': 18, 'ops': [['add', 2], ['add', 20], ['has', 38], ['has', 3], ['has', 2]]},
[['added', 'added', False, False, True],
[0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['normal add and remove',
{'k': 2, 'm': 18, 'ops': [['add', 35], ['add', 36], ['remove', 35], ['has', 35], ['has', 36]]},
[['added', 'added', 'removed', False, True],
[1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['remove absent from empty',
{'k': 2, 'm': 18, 'ops': [['remove', 9], ['has', 9]]},
[['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]],
['saturated then drained',
{'k': 1,
'm': 18,
'ops': [['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['add', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['remove', 6],
['has', 6]]},
[['added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'added',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
'removed',
True],
[0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]]]]
for label, args, expected in cases[N - 1]:
check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)
| Boundary fixture | Actual | Expected | Outcome |
|---|---|---|---|
| duplicate probe positions | [['added', 'added', True, 'removed', False, True], [0, 1, 1, 1, 1, 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]] | Passed |
| hot item with repeated positions | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| wide stride item | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0]] | [['added', 'added', True, 'removed'], [0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0]] | Failed |
| saturating counter | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', True], [0, 0, 0, 0, 15, 15, 0, 0, 0, 0, 0, 0]] | Passed |
| atomic removal of absent item | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | [['added', 'absent', True], [0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0]] | Passed |
| partial overlap membership | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | [['added', 'added', False, False, True], [0, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 0]] | Passed |
| normal add and remove | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | [['added', 'added', 'removed', False, True], [0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1]] | Passed |
| remove absent from empty | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | [['absent', False], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] | Passed |
| saturated then drained | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', True], [0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]] | [['added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'added', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', 'removed', True], [0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0]] | Passed |
SHA-256 / 24cc8852289710f6f76832e52080662d662b425b60ea6cb39b4d424908d098d5
HELD IN THE MEMBER ARCHIVE
The verified repair and its recorded checks are member-only.
This mechanism has 9 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.
Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.
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Sign in to the archive ↗Verification & scope
A deterministic, bounded teaching model with stipulated constants and pre-hashed or explicitly hashed inputs; it is not a production implementation and makes no claim of conformance to any library or paper beyond the stated contract. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.
Observations recorded using Python 3.12.14 at 2026-09-29T14:48:43.024511+00:00.
Case digest / 0ab2aae62a1d0bb651085c6666cd16874be9f9f18838e797be06ff72e641b636