FA-92056 / PLC ladder logic scan cycles / Open access

A trigger at the exact completion time is counted as a task overlap · case 01

Periodic tasks whose execution equals the period are skipped every other cycle and the overlap counter climbs.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The overlap test uses trigger <= completion time.

VERIFIED REPAIR

Only a trigger strictly before the previous completion is an overlap.

Unsuccessful approach: Exempting the first trigger still treats a back-to-back completion as an overlap.

Case contract

Periodic task triggered every period ms from t=0; exec_times[k] is how long the k-th triggered execution would take. A trigger arriving while the previous execution is still running (trigger time < completion time) is an overlap: it is counted and skipped, not queued; a trigger exactly at completion starts normally. An execution longer than watchdog raises a major fault at start + watchdog and scheduling stops. Return [start_times, overlap_count, fault_time or None].

Why this case matters

Ladder programs are executed as repeated scans; each defect here changes what a rung, timer, counter or data-table instruction reports on a particular scan, which is how commissioning and field faults are actually observed.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(period, watchdog, exec_times):
    t_free = 0
    starts = []
    overlaps = 0
    fault = None
    for k, ex in enumerate(exec_times):
        trig = k * period
        if trig <= t_free:
            overlaps += 1
            continue
        starts.append(trig)
        if ex > watchdog:
            fault = trig + watchdog
            break
        t_free = trig + ex
    return [starts, overlaps, fault]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: scenario 1', [50, 100, [100, 100, 100, 100, 50, 25]], [[0, 100, 200, 250], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 2', [20, 100, [100, 100, 60, 39, 20, 40, 54, 40]], [[0, 100, 140], 5, None]],
  ['regression: scenario 3', [50, 40, [50, 100, 50, 100, 100, 40]], [[0], 0, 40]]],
 [['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: scenario 1', [20, 60, [60, 20, 36, 40, 20]], [[0, 60], 3, None]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 2',
   [10, 100, [10, 10, 10, 10, 10, 20, 100, 3, 20, 10, 100]],
   [[0, 10, 20, 30, 40, 50, 70, 80, 100], 2, None]],
  ['regression: scenario 3', [20, 100, [40, 40, 51, 40, 100]], [[0, 40], 3, None]]],
 [['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: scenario 3',
   [20, 30, [20, 30, 6, 30, 40, 39, 61, 36, 40, 40, 30, 20]],
   [[0, 20, 60, 100], 2, 130]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 1', [20, 100, [100, 20, 60, 100, 40, 20, 30, 12]], [[0, 100, 120], 5, None]],
  ['regression: scenario 2', [10, 40, [50, 40, 10, 40, 10, 61, 60, 40, 20, 20, 10, 10]], [[0], 0, 40]]],
 [['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: scenario 3',
   [10, 40, [20, 20, 20, 20, 10, 61, 55, 66, 20, 37, 40, 40]],
   [[0, 20, 40, 50], 2, 90]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 1',
   [20, 30, [21, 20, 20, 20, 40, 30, 20, 30, 40, 30, 40]],
   [[0, 40, 60, 80], 1, 110]],
  ['regression: scenario 2',
   [50, 100, [100, 100, 100, 50, 100, 50, 100, 50, 100, 15, 100, 50]],
   [[0, 100, 200, 300, 400, 500], 6, None]]],
 [['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 10',
   [10, 40, [40, 40, 40, 20, 10, 40, 14, 21, 20, 40, 41, 10]],
   [[0, 40, 50, 90], 8, None]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: scenario 1', [25, 60, [70, 25, 60, 35, 25, 15, 60, 60, 25, 50, 25, 4]], [[0], 0, 60]],
  ['regression: scenario 2', [20, 30, [40, 33, 50, 20, 40, 30, 30, 29, 30, 68, 20]], [[0], 0, 30]]]]
for label, args, expected in fixtures[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
regression: mixed overlaps	`[[10, 30, 50], 3, None]`	`[[0, 10, 30, 40], 2, None]`	Failed
regression: scenario 1	`[[50, 200], 4, None]`	`[[0, 100, 200, 250], 2, None]`	Failed
regression: watchdog exceeded	`[[10], 1, 22]`	`[[0, 10], 0, 22]`	Failed
regression: exact watchdog	`[[20, 40, 60], 1, None]`	`[[0, 40, 60], 1, None]`	Failed
regression: first execution overruns	`[[10], 1, None]`	`[[0], 0, 25]`	Failed
regression: skip then drift	`[[10, 20, 30, 40, 50], 1, None]`	`[[0, 30, 40, 50], 2, None]`	Failed
regression: scenario 2	`[[20, 140], 6, None]`	`[[0, 100, 140], 5, None]`	Failed
regression: scenario 3	`[[50], 1, 90]`	`[[0], 0, 40]`	Failed

SHA-256 / af78ce1958cfbd0c6dca293fcf941282dcc57fd2ffde5a5e18824a1e4b19d672

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(period, watchdog, exec_times):
    t_free = 0
    starts = []
    overlaps = 0
    fault = None
    for k, ex in enumerate(exec_times):
        trig = k * period
        if k and trig <= t_free:
            overlaps += 1
            continue
        starts.append(trig)
        if ex > watchdog:
            fault = trig + watchdog
            break
        t_free = trig + ex
    return [starts, overlaps, fault]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: scenario 1', [50, 100, [100, 100, 100, 100, 50, 25]], [[0, 100, 200, 250], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 2', [20, 100, [100, 100, 60, 39, 20, 40, 54, 40]], [[0, 100, 140], 5, None]],
  ['regression: scenario 3', [50, 40, [50, 100, 50, 100, 100, 40]], [[0], 0, 40]]],
 [['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: scenario 1', [20, 60, [60, 20, 36, 40, 20]], [[0, 60], 3, None]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 2',
   [10, 100, [10, 10, 10, 10, 10, 20, 100, 3, 20, 10, 100]],
   [[0, 10, 20, 30, 40, 50, 70, 80, 100], 2, None]],
  ['regression: scenario 3', [20, 100, [40, 40, 51, 40, 100]], [[0, 40], 3, None]]],
 [['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: scenario 3',
   [20, 30, [20, 30, 6, 30, 40, 39, 61, 36, 40, 40, 30, 20]],
   [[0, 20, 60, 100], 2, 130]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 1', [20, 100, [100, 20, 60, 100, 40, 20, 30, 12]], [[0, 100, 120], 5, None]],
  ['regression: scenario 2', [10, 40, [50, 40, 10, 40, 10, 61, 60, 40, 20, 20, 10, 10]], [[0], 0, 40]]],
 [['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: scenario 3',
   [10, 40, [20, 20, 20, 20, 10, 61, 55, 66, 20, 37, 40, 40]],
   [[0, 20, 40, 50], 2, 90]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 1',
   [20, 30, [21, 20, 20, 20, 40, 30, 20, 30, 40, 30, 40]],
   [[0, 40, 60, 80], 1, 110]],
  ['regression: scenario 2',
   [50, 100, [100, 100, 100, 50, 100, 50, 100, 50, 100, 15, 100, 50]],
   [[0, 100, 200, 300, 400, 500], 6, None]]],
 [['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 10',
   [10, 40, [40, 40, 40, 20, 10, 40, 14, 21, 20, 40, 41, 10]],
   [[0, 40, 50, 90], 8, None]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: scenario 1', [25, 60, [70, 25, 60, 35, 25, 15, 60, 60, 25, 50, 25, 4]], [[0], 0, 60]],
  ['regression: scenario 2', [20, 30, [40, 33, 50, 20, 40, 30, 30, 29, 30, 68, 20]], [[0], 0, 30]]]]
for label, args, expected in fixtures[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
regression: mixed overlaps	`[[0, 10, 30, 50], 2, None]`	`[[0, 10, 30, 40], 2, None]`	Failed
regression: scenario 1	`[[0, 150], 4, None]`	`[[0, 100, 200, 250], 2, None]`	Failed
regression: watchdog exceeded	`[[0, 10], 0, 22]`	`[[0, 10], 0, 22]`	Passed
regression: exact watchdog	`[[0, 40, 60], 1, None]`	`[[0, 40, 60], 1, None]`	Passed
regression: first execution overruns	`[[0], 0, 25]`	`[[0], 0, 25]`	Passed
regression: skip then drift	`[[0, 30, 40, 50], 2, None]`	`[[0, 30, 40, 50], 2, None]`	Passed
regression: scenario 2	`[[0, 120], 6, None]`	`[[0, 100, 140], 5, None]`	Failed
regression: scenario 3	`[[0], 0, 40]`	`[[0], 0, 40]`	Passed

SHA-256 / f341de25bd553a30ab94b609ec5666be297c6acf263089b3a0812baaaecb18fe

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(period, watchdog, exec_times):
    t_free = 0
    starts = []
    overlaps = 0
    fault = None
    for k, ex in enumerate(exec_times):
        trig = k * period
        if trig < t_free:
            overlaps += 1
            continue
        starts.append(trig)
        if ex > watchdog:
            fault = trig + watchdog
            break
        t_free = trig + ex
    return [starts, overlaps, fault]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: scenario 1', [50, 100, [100, 100, 100, 100, 50, 25]], [[0, 100, 200, 250], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 2', [20, 100, [100, 100, 60, 39, 20, 40, 54, 40]], [[0, 100, 140], 5, None]],
  ['regression: scenario 3', [50, 40, [50, 100, 50, 100, 100, 40]], [[0], 0, 40]]],
 [['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: scenario 1', [20, 60, [60, 20, 36, 40, 20]], [[0, 60], 3, None]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 2',
   [10, 100, [10, 10, 10, 10, 10, 20, 100, 3, 20, 10, 100]],
   [[0, 10, 20, 30, 40, 50, 70, 80, 100], 2, None]],
  ['regression: scenario 3', [20, 100, [40, 40, 51, 40, 100]], [[0, 40], 3, None]]],
 [['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: scenario 3',
   [20, 30, [20, 30, 6, 30, 40, 39, 61, 36, 40, 40, 30, 20]],
   [[0, 20, 60, 100], 2, 130]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 1', [20, 100, [100, 20, 60, 100, 40, 20, 30, 12]], [[0, 100, 120], 5, None]],
  ['regression: scenario 2', [10, 40, [50, 40, 10, 40, 10, 61, 60, 40, 20, 20, 10, 10]], [[0], 0, 40]]],
 [['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: scenario 3',
   [10, 40, [20, 20, 20, 20, 10, 61, 55, 66, 20, 37, 40, 40]],
   [[0, 20, 40, 50], 2, 90]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 1',
   [20, 30, [21, 20, 20, 20, 40, 30, 20, 30, 40, 30, 40]],
   [[0, 40, 60, 80], 1, 110]],
  ['regression: scenario 2',
   [50, 100, [100, 100, 100, 50, 100, 50, 100, 50, 100, 15, 100, 50]],
   [[0, 100, 200, 300, 400, 500], 6, None]]],
 [['regression: skip then drift', [10, 100, [25, 1, 1, 1, 1, 1]], [[0, 30, 40, 50], 2, None]],
  ['regression: scenario 10',
   [10, 40, [40, 40, 40, 20, 10, 40, 14, 21, 20, 40, 41, 10]],
   [[0, 40, 50, 90], 8, None]],
  ['regression: mixed overlaps', [10, 50, [5, 15, 3, 10, 12, 4]], [[0, 10, 30, 40], 2, None]],
  ['regression: watchdog exceeded', [10, 12, [5, 13, 4]], [[0, 10], 0, 22]],
  ['regression: exact watchdog', [20, 30, [30, 5, 5, 5]], [[0, 40, 60], 1, None]],
  ['regression: first execution overruns', [10, 25, [30, 5]], [[0], 0, 25]],
  ['regression: scenario 1', [25, 60, [70, 25, 60, 35, 25, 15, 60, 60, 25, 50, 25, 4]], [[0], 0, 60]],
  ['regression: scenario 2', [20, 30, [40, 33, 50, 20, 40, 30, 30, 29, 30, 68, 20]], [[0], 0, 30]]]]
for label, args, expected in fixtures[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
regression: mixed overlaps	`[[0, 10, 30, 40], 2, None]`	`[[0, 10, 30, 40], 2, None]`	Passed
regression: scenario 1	`[[0, 100, 200, 250], 2, None]`	`[[0, 100, 200, 250], 2, None]`	Passed
regression: watchdog exceeded	`[[0, 10], 0, 22]`	`[[0, 10], 0, 22]`	Passed
regression: exact watchdog	`[[0, 40, 60], 1, None]`	`[[0, 40, 60], 1, None]`	Passed
regression: first execution overruns	`[[0], 0, 25]`	`[[0], 0, 25]`	Passed
regression: skip then drift	`[[0, 30, 40, 50], 2, None]`	`[[0, 30, 40, 50], 2, None]`	Passed
regression: scenario 2	`[[0, 100, 140], 5, None]`	`[[0, 100, 140], 5, None]`	Passed
regression: scenario 3	`[[0], 0, 40]`	`[[0], 0, 40]`	Passed

SHA-256 / 0df9b788a94f1879653922cb63cdc81e10c3f111466f8b524d4e8f303f1ab3fa

Verification & scope

A deterministic bounded teaching model of one PLC instruction or rung pattern evaluated scan by scan. The stated contract is a stipulated toy convention, not a claim of conformance to any vendor controller or IEC 61131-3 runtime. 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 2026-09-29T14:51:42.030941+00:00.

Case digest / f5d61068f7c8c393c32b9970b2cca8c61ce2977a20ce4a9d120fc124da8d2376