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+---
+layout: page
+title:  "Counters"
+by: "Aviral Goel"
+---
+
+Counters are replicated integers. They are the most basic distributed object. This chapter describes the different variations of counter CRDT in both state based and operation based form.
+
+## G-counter - Increment only counter
+
+As the name suggests, these counters only support increment operation. They can be used to implement the `like` button functionality of social media websites.
+
+### CmRDT: Operation based G-counter
+
+In the operation based implementation, the increment operation is transmitted to all other replicas. 
+This is straightforward to implement as there is only one update operation. 
+
+#### Specification
+
+
+#### Figure
+
+![Operation based increment only counter][operation-based-increment-only-counter]
+
+
+### CvRDT: State based specification
+
+In the state based implementation, the counter state is transmitted to all other replicas.
+But how do we model the state? Of course, the counter's count is its state. 
+Since the count always increases, modeling the state as count automatically makes it a monotonic semilattice.
+
+#### Specification
+
+
+#### Figure
+
+![State based increment only counter (incorrect)][state-based-increment-only-counter-incorrect]
+As it can be seen from the figure, the clients issue a total of 4 increment requests. However, the replicas finally converge to 2.
+Something is clearly amiss! When two replicas are incremented, they should together converge to 2. But the `merge` function computes the maximum of two states. 
+
+
+#### Specification
+
+
+#### Figure
+
+![State based increment only counter (correct)][state-based-increment-only-counter-correct]
+
+As it can be seen from the figure, the clients issue a total of 4 increment requests. However, the replicas finally converge to 2.
+Something is clearly amiss! When two replicas are incremented, they should together converge to 2. But the `merge` function computes the maximum of two states. 
+
+
+
+
+
+## PN-counter - Increment and Decrement counter
+
+### CmRDT: Operation based specification
+
+#### Specification
+
+#### Figure
+
+![Operation based increment and decrement counter][operation-based-increment-and-decrement-counter]
+
+### CvRDT: State based specification
+
+#### Specification
+
+
+
+#### Figure
+
+![State based increment and decrement counter (incorrect)][state-based-increment-and-decrement-counter-incorrect]
+
+
+
+#### Specification
+
+
+
+#### Figure
+
+![State based increment and decrement counter (correct)][state-based-increment-and-decrement-counter-correct]
+
+## Non-negative Counter
+
+
+
+
+
+### State based specification (CmRDT)
+
+```javascript
+class 
+    counts = [0, 0, ..., 0]
+    
+    update increment()
+        g <- getId()
+        counts[g] <- counts[g] + 1
+    
+    // query function
+    function value():
+        sum = 0
+        for count in counts:
+            sum <- sum + count
+        return sum
+    
+    function compare(other):
+        for i in 0 : length(replicas()):
+            if counts[i] > other.counts[i]:
+                return False
+        return True
+    
+```
+
+[operation-based-increment-only-counter]: images/counters/operation-based-increment-only-counter.png
+[state-based-increment-only-counter-incorrect]: images/counters/state-based-increment-only-counter-incorrect.png
+[state-based-increment-only-counter-correct]: images/counters/state-based-increment-only-counter-correct.png
+[operation-based-increment-and-decrement-counter]: images/counters/operation-based-increment-and-decrement-counter.png
+[state-based-increment-and-decrement-counter-incorrect]: images/counters/state-based-increment-and-decrement-counter-incorrect.png
+[state-based-increment-and-decrement-counter-correct]: images/counters/state-based-increment-and-decrement-counter-correct.png
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