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# What is a causal inference?

Anjana Shankar

## Overview

Causality is the relationship between a cause and effect. In distributed systems, ordering of events is challenging, as timestamps across nodes cannot be compared. This is where causality is useful in the distributed system.

### Causality and the happens-before relationship

Let’s define an event as something happening at one node. This something can be either sending or receiving a message or a local execution step.

An Event A is said to have happened before an Event B if, and only if, the following holds true:

1. A and B occurred on the same node, and A occurred before B in that node’s local execution order.
2. A is the sending of some message, and B is the receipt of that same message.
3. There exists an event C such that A happened before C and C happened before B, as per conditions 1 and 2.

The happens-before relationship is a way to determine causality in a distributed system.

In the figure above, we see:

• B -> C: The B denotes the sending of message M1, and C denotes the receiving of the same message.
• C -> D: They are events on the same node.
• D -> E: The D denotes the sending of message M2 and E denotes the receiving of the same message.

Thus, we have a causal relationship A -> B -> C -> D -> E.

As there is no chain of events that can determine a relationship between A and F, we say that A||F, which means A is concurrent with F.

### Conclusion

The event ordering process in the distributed system uses the notion of causality. This forms the base for most distributed system algorithms.

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Anjana Shankar
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