Structures
PN-counter
Alice, Bob, and Carol have agreed on 10 birds. Then Alice finds 3 more while Bob finds a duplicate sighting. Their G-counter notebooks cannot erase a count, so each hiker adds a second grow-only table for corrections.
Each hiker carries the same two-page notebook
The first page is the positive counter, or P. It records
new bird sightings. The second page is the negative counter, or
N. It records sightings that must be subtracted. Each page
has one row that only Alice fills in, one for Bob, and one for Carol.
| Notebook page | Row | Starting value |
|---|---|---|
| Sightings (P) | Agreed count | 10 |
| Sightings (P) | Alice | 0 |
| Sightings (P) | Bob | 0 |
| Sightings (P) | Carol | 0 |
| Corrections (N) | Alice | 0 |
| Corrections (N) | Bob | 0 |
| Corrections (N) | Carol | 0 |
Alice writes 3 in her row on the sightings page. Bob writes 1 in his
row on the corrections page. The note does not ask another hiker to
apply +3 or -1 again. It reports the page,
the row, and the cumulative value now written there.
Alice Sightings page · Alice row
Bob Corrections page · Bob row
Add a second G-counter
Bob spots a mistake: one line records the same bird twice. The shared count must fall by one.
A G-counter component can only grow. Bob cannot lower his component because an older note with the larger value could arrive later and restore the mistake.
A PN-counter records the correction in a second G-counter. The positive counter records sightings. The negative counter records corrections. Both counters still grow and merge each hiker's component by maximum.
P = sightings G-counter
N = corrections G-counter
birds = P - N
The hikers count in both directions without making either G-counter
count backward. They increment P for a new bird and
increment N for a correction.
Alice and Bob fill in different pages
Neither hiker has received the other's note. Alice's notebook has 13 sightings and no corrections, so she reads 13. Bob's has 10 sightings and 1 correction, so he reads 9. Carol has not found either note, so she still reads 10.
| Notebook entry | Alice | Bob | Carol |
|---|---|---|---|
| Agreed sightings | 10 | 10 | 10 |
| Alice sightings row | 3 | 0 | 0 |
| Bob corrections row | 0 | 1 | 0 |
| Birds seen (P - N) | 13 | 9 | 10 |
When both notes arrive, every notebook contains 3 in Alice's sightings
row and 1 in Bob's corrections row. The notes can arrive in either order:
10 + 3 - 1 and 10 - 1 + 3 both equal
12. Each page keeps the G-counter merge rule, so a hiker
who finds the same note twice still writes the cumulative value only
once.
Correct the shared bird count
The hikers agree on 10 birds. As soon as a hiker records a new sighting or correction, it is sent through the known checkpoint.
Merge rule Keep the largest sightings and corrections from each hiker.
New note In transit to a checkpoint
Shared note Being delivered to the other hikers
Alice
Agreed count received
Birds in this hiker's view
Bob
Agreed count received
Birds in this hiker's view
Carol
Agreed count received
Birds in this hiker's view
- No correction note shared yet.
Enable JavaScript to run the demo. The starting count and expected result remain available in the article.
Run the correction race, or record new birds and corrections for any hiker.
Open the hikers' two notebook tables
Each hiker's notebook has a sightings table for the positive G-counter and a corrections table for the negative G-counter. Both tables only grow and merge by per-hiker maximum.
birds = P - N| Sightings from | Alice's view | Bob's view | Carol's view |
|---|---|---|---|
| Agreed starting count | 10 | 10 | 10 |
| Alice | 0 | 0 | 0 |
| Bob | 0 | 0 | 0 |
| Carol | 0 | 0 | 0 |
| Corrections from | Alice's view | Bob's view | Carol's view |
|---|---|---|---|
| Alice | 0 | 0 | 0 |
| Bob | 0 | 0 | 0 |
| Carol | 0 | 0 | 0 |
The correction survives the merge
After both notes arrive, the positive G-counter totals 13 and the
negative G-counter totals 1. Alice, Bob, and Carol all compute
P - N = 13 - 1 = 12.
Delivery order does not change that result, and a repeated note does
not apply the correction twice.
A PN-counter can also produce a negative value. That is correct counter behavior, but it may be invalid for the thing being counted. An application that must never show fewer than zero birds needs another rule to prevent or coordinate those updates.
Sources and implementation
This lesson calls Watershed's public PN-counter kernel and sends the three hikers' notes through Sluice, Watershed's in-memory server for a collaborative document.
The merge rule follows the state-based positive-negative counter described in A comprehensive study of Convergent and Commutative Replicated Data Types.