FA-73681 / Rate limiter algorithms / Open access
Priority limiter with reserved high-priority capacity: high counter never resets · case 01
After a few windows the high counter alone fills capacity and everything is denied.
ROOT CAUSE
The window change resets only the low counter.
VERIFIED REPAIR
Reset both counters when the window changes.
Unsuccessful approach: Resetting only the high counter lets low usage accumulate across windows.
Case contract
Input {capacity, reserved_high, requests [[t_ms, priority]]} with nondecreasing t, one-second epoch windows. Only the exact label "high" is high priority; every other label is low. A high request is admitted while total admitted < capacity. A low request is admitted only while admitted low < capacity - reserved_high and total < capacity. Both counters reset each window. Return [decisions, [low, high] of the final window].
Why this case matters
Shared limiters reserve headroom for critical traffic (health checks, payments) so that bulk clients cannot starve it; the reserve arithmetic decides whether the guarantee holds.
1 / The failure
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
cap = x['capacity']
res = x['reserved_high']
win = None
low = high = 0
out = []
for t, prio in x['requests']:
w = t // 1000
if w != win:
win, low = w, 0
if prio == 'high':
ok = low + high < cap
else:
ok = low < cap - res and low + high < cap
if ok:
if prio == 'high':
high += 1
else:
low += 1
out.append('allow')
else:
out.append('deny')
return [out, [low, high]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[4, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [8, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [4, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [5, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1003, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[1, 'low'],
[1, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[23, 'low'],
[30, 'batch'],
[460, 'batch'],
[783, 'low'],
[807, 'high'],
[926, 'low'],
[1133, 'low'],
[1169, 'low'],
[1221, 'high'],
[1686, 'low'],
[1702, 'low'],
[1740, 'low'],
[2424, 'low'],
[2472, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'allow',
'deny',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow'],
[1, 1]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[5, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [9, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [5, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [6, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1004, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[2, 'low'],
[2, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[284, 'batch'],
[629, 'low'],
[787, 'low'],
[903, 'low'],
[1032, 'batch'],
[1118, 'high'],
[1495, 'low'],
[1855, 'low'],
[1876, 'low'],
[1919, 'batch'],
[2238, 'high'],
[2382, 'batch'],
[2390, 'high'],
[2492, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow',
'allow',
'allow'],
[1, 3]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[6, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [10, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [6, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [7, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1005, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[3, 'low'],
[3, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[99, 'low'],
[696, 'low'],
[811, 'batch'],
[837, 'low'],
[912, 'batch'],
[1070, 'low'],
[1174, 'batch'],
[1400, 'batch'],
[1530, 'low'],
[1887, 'high'],
[1994, 'batch'],
[2235, 'low'],
[2286, 'low'],
[2369, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow',
'deny',
'deny',
'allow',
'deny',
'allow',
'allow',
'allow'],
[2, 1]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[7, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [11, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [7, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [8, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1006, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[4, 'low'],
[4, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[279, 'high'],
[550, 'high'],
[665, 'low'],
[940, 'low'],
[1010, 'batch'],
[1022, 'low'],
[1597, 'low'],
[1623, 'batch'],
[1749, 'low'],
[1850, 'low'],
[2025, 'high'],
[2095, 'high'],
[2322, 'low'],
[2325, 'low']],
'reserved_high': 2},
[['allow',
'allow',
'allow',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'deny',
'allow',
'allow',
'allow',
'allow'],
[2, 2]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[8, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [12, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [8, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [9, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1007, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[5, 'low'],
[5, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[249, 'low'],
[476, 'low'],
[620, 'high'],
[621, 'high'],
[646, 'batch'],
[704, 'low'],
[832, 'batch'],
[989, 'batch'],
[1004, 'batch'],
[1140, 'low'],
[1764, 'low'],
[2209, 'high'],
[2225, 'batch'],
[2378, 'batch']],
'reserved_high': 2},
[['allow',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'deny',
'allow',
'allow',
'deny',
'allow',
'allow',
'allow'],
[2, 1]]]]]
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 |
|---|---|---|---|
| low traffic cannot take reserve | [['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]] | [['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]] | Passed |
| high traffic blocks low at capacity | [['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]] | [['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]] | Passed |
| unknown priority is low | [['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]] | [['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]] | Passed |
| custom label cannot claim reserve | [['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]] | [['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]] | Passed |
| window reset clears both | [['allow', 'allow', 'deny', 'deny', 'deny', 'deny'], [0, 2]] | [['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]] | Failed |
| mixed within reserve | [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]] | [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]] | Passed |
| random mix | [['allow', 'allow', 'deny', 'deny', 'allow', 'deny', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny', 'allow', 'allow'], [1, 3]] | [['allow', 'allow', 'deny', 'deny', 'allow', 'deny', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny', 'allow', 'allow'], [1, 1]] | Failed |
SHA-256 / 1d386a2cd1835e4383487293c536875f9470c089dba3ca95c29de915f09d9c99
2 / The unsuccessful fix
Exit 1"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
cap = x['capacity']
res = x['reserved_high']
win = None
low = high = 0
out = []
for t, prio in x['requests']:
w = t // 1000
if w != win:
win, high = w, 0
if prio == 'high':
ok = low + high < cap
else:
ok = low < cap - res and low + high < cap
if ok:
if prio == 'high':
high += 1
else:
low += 1
out.append('allow')
else:
out.append('deny')
return [out, [low, high]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[4, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [8, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [4, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [5, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1003, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[1, 'low'],
[1, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[23, 'low'],
[30, 'batch'],
[460, 'batch'],
[783, 'low'],
[807, 'high'],
[926, 'low'],
[1133, 'low'],
[1169, 'low'],
[1221, 'high'],
[1686, 'low'],
[1702, 'low'],
[1740, 'low'],
[2424, 'low'],
[2472, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'allow',
'deny',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow'],
[1, 1]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[5, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [9, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [5, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [6, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1004, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[2, 'low'],
[2, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[284, 'batch'],
[629, 'low'],
[787, 'low'],
[903, 'low'],
[1032, 'batch'],
[1118, 'high'],
[1495, 'low'],
[1855, 'low'],
[1876, 'low'],
[1919, 'batch'],
[2238, 'high'],
[2382, 'batch'],
[2390, 'high'],
[2492, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow',
'allow',
'allow'],
[1, 3]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[6, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [10, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [6, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [7, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1005, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[3, 'low'],
[3, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[99, 'low'],
[696, 'low'],
[811, 'batch'],
[837, 'low'],
[912, 'batch'],
[1070, 'low'],
[1174, 'batch'],
[1400, 'batch'],
[1530, 'low'],
[1887, 'high'],
[1994, 'batch'],
[2235, 'low'],
[2286, 'low'],
[2369, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow',
'deny',
'deny',
'allow',
'deny',
'allow',
'allow',
'allow'],
[2, 1]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[7, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [11, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [7, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [8, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1006, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[4, 'low'],
[4, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[279, 'high'],
[550, 'high'],
[665, 'low'],
[940, 'low'],
[1010, 'batch'],
[1022, 'low'],
[1597, 'low'],
[1623, 'batch'],
[1749, 'low'],
[1850, 'low'],
[2025, 'high'],
[2095, 'high'],
[2322, 'low'],
[2325, 'low']],
'reserved_high': 2},
[['allow',
'allow',
'allow',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'deny',
'allow',
'allow',
'allow',
'allow'],
[2, 2]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[8, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [12, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [8, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [9, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1007, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[5, 'low'],
[5, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[249, 'low'],
[476, 'low'],
[620, 'high'],
[621, 'high'],
[646, 'batch'],
[704, 'low'],
[832, 'batch'],
[989, 'batch'],
[1004, 'batch'],
[1140, 'low'],
[1764, 'low'],
[2209, 'high'],
[2225, 'batch'],
[2378, 'batch']],
'reserved_high': 2},
[['allow',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'deny',
'allow',
'allow',
'deny',
'allow',
'allow',
'allow'],
[2, 1]]]]]
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 |
|---|---|---|---|
| low traffic cannot take reserve | [['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]] | [['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]] | Passed |
| high traffic blocks low at capacity | [['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]] | [['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]] | Passed |
| unknown priority is low | [['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]] | [['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]] | Passed |
| custom label cannot claim reserve | [['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]] | [['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]] | Passed |
| window reset clears both | [['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]] | [['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]] | Passed |
| mixed within reserve | [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]] | [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]] | Passed |
| random mix | [['allow', 'allow', 'deny', 'deny', 'allow', 'deny', 'deny', 'deny', 'allow', 'deny', 'deny', 'deny', 'deny', 'allow'], [2, 1]] | [['allow', 'allow', 'deny', 'deny', 'allow', 'deny', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny', 'allow', 'allow'], [1, 1]] | Failed |
SHA-256 / c6b9461f892acf8ba607a57b0666dfc90848dd61d48d06d02070eb18a93343d3
3 / The verified repair
Exit 0"""Failure Map reference implementation. Python standard library only."""
import json
N = 1
observations = []
def solve(x):
cap = x['capacity']
res = x['reserved_high']
win = None
low = high = 0
out = []
for t, prio in x['requests']:
w = t // 1000
if w != win:
win, low, high = w, 0, 0
if prio == 'high':
ok = low + high < cap
else:
ok = low < cap - res and low + high < cap
if ok:
if prio == 'high':
high += 1
else:
low += 1
out.append('allow')
else:
out.append('deny')
return [out, [low, high]]
def check(label, actual, expected):
observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
cases = [[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[4, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [8, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [4, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [5, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1003, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[1, 'low'],
[1, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[23, 'low'],
[30, 'batch'],
[460, 'batch'],
[783, 'low'],
[807, 'high'],
[926, 'low'],
[1133, 'low'],
[1169, 'low'],
[1221, 'high'],
[1686, 'low'],
[1702, 'low'],
[1740, 'low'],
[2424, 'low'],
[2472, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'allow',
'deny',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow'],
[1, 1]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[5, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [9, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [5, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [6, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1004, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[2, 'low'],
[2, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[284, 'batch'],
[629, 'low'],
[787, 'low'],
[903, 'low'],
[1032, 'batch'],
[1118, 'high'],
[1495, 'low'],
[1855, 'low'],
[1876, 'low'],
[1919, 'batch'],
[2238, 'high'],
[2382, 'batch'],
[2390, 'high'],
[2492, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow',
'allow',
'allow'],
[1, 3]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[6, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [10, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [6, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [7, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1005, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[3, 'low'],
[3, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[99, 'low'],
[696, 'low'],
[811, 'batch'],
[837, 'low'],
[912, 'batch'],
[1070, 'low'],
[1174, 'batch'],
[1400, 'batch'],
[1530, 'low'],
[1887, 'high'],
[1994, 'batch'],
[2235, 'low'],
[2286, 'low'],
[2369, 'high']],
'reserved_high': 2},
[['allow',
'allow',
'deny',
'deny',
'deny',
'allow',
'allow',
'deny',
'deny',
'allow',
'deny',
'allow',
'allow',
'allow'],
[2, 1]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[7, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [11, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [7, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [8, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1006, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[4, 'low'],
[4, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[279, 'high'],
[550, 'high'],
[665, 'low'],
[940, 'low'],
[1010, 'batch'],
[1022, 'low'],
[1597, 'low'],
[1623, 'batch'],
[1749, 'low'],
[1850, 'low'],
[2025, 'high'],
[2095, 'high'],
[2322, 'low'],
[2325, 'low']],
'reserved_high': 2},
[['allow',
'allow',
'allow',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'deny',
'allow',
'allow',
'allow',
'allow'],
[2, 2]]]],
[['low traffic cannot take reserve',
{'capacity': 5,
'requests': [[0, 'low'],
[0, 'low'],
[0, 'low'],
[0, 'low'],
[1, 'high'],
[2, 'high'],
[8, 'high'],
[4, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]]],
['high traffic blocks low at capacity',
{'capacity': 4,
'requests': [[0, 'high'], [0, 'high'], [0, 'high'], [5, 'low'], [6, 'low'], [12, 'low']],
'reserved_high': 1},
[['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]]],
['unknown priority is low',
{'capacity': 3,
'requests': [[0, 'batch'], [1, 'critical'], [2, 'batch'], [8, 'high'], [4, 'critical']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]]],
['custom label cannot claim reserve',
{'capacity': 4,
'requests': [[0, 'batch'], [1, 'batch'], [2, 'critical'], [3, 'high'], [9, 'high']],
'reserved_high': 2},
[['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]]],
['window reset clears both',
{'capacity': 2,
'requests': [[0, 'high'],
[1, 'high'],
[999, 'low'],
[1000, 'high'],
[1001, 'low'],
[1007, 'high']],
'reserved_high': 1},
[['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]]],
['mixed within reserve',
{'capacity': 6,
'requests': [[0, 'high'],
[0, 'low'],
[0, 'high'],
[0, 'low'],
[0, 'low'],
[5, 'low'],
[5, 'high']],
'reserved_high': 3},
[['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]]],
['random mix',
{'capacity': 4,
'requests': [[249, 'low'],
[476, 'low'],
[620, 'high'],
[621, 'high'],
[646, 'batch'],
[704, 'low'],
[832, 'batch'],
[989, 'batch'],
[1004, 'batch'],
[1140, 'low'],
[1764, 'low'],
[2209, 'high'],
[2225, 'batch'],
[2378, 'batch']],
'reserved_high': 2},
[['allow',
'allow',
'allow',
'allow',
'deny',
'deny',
'deny',
'deny',
'allow',
'allow',
'deny',
'allow',
'allow',
'allow'],
[2, 1]]]]]
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 |
|---|---|---|---|
| low traffic cannot take reserve | [['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]] | [['allow', 'allow', 'allow', 'deny', 'allow', 'allow', 'deny', 'deny'], [3, 2]] | Passed |
| high traffic blocks low at capacity | [['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]] | [['allow', 'allow', 'allow', 'allow', 'deny', 'deny'], [1, 3]] | Passed |
| unknown priority is low | [['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]] | [['allow', 'allow', 'deny', 'allow', 'deny'], [2, 1]] | Passed |
| custom label cannot claim reserve | [['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]] | [['allow', 'allow', 'deny', 'allow', 'allow'], [2, 2]] | Passed |
| window reset clears both | [['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]] | [['allow', 'allow', 'deny', 'allow', 'allow', 'deny'], [1, 1]] | Passed |
| mixed within reserve | [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]] | [['allow', 'allow', 'allow', 'allow', 'allow', 'deny', 'allow'], [3, 3]] | Passed |
| random mix | [['allow', 'allow', 'deny', 'deny', 'allow', 'deny', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny', 'allow', 'allow'], [1, 1]] | [['allow', 'allow', 'deny', 'deny', 'allow', 'deny', 'allow', 'allow', 'allow', 'deny', 'deny', 'deny', 'allow', 'allow'], [1, 1]] | Passed |
SHA-256 / 92e658a00a05b3fed2ae53992993c753ba5a6f179aa28bf20adc1a9c1da31f76
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 2026-09-29T14:48:49.815050+00:00.
Case digest / f215ee7265c814da91f7478700ab20bb5a4a0aefac54369f9c5adf1e398dee09