**A DAG-Based Cryptocurrency Framework**

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*This is a transcript of Christopher Carr’s presentation at Master Workshop: Layer 1 solutions, which took place at **Primalbase AMS**.*

What’s a DAG? My talk will go along these lines. An introduction - what is a DAG and why do we want to use them? Then I will talk about the Graphchain framework, which was originally a STAG-based framework that we wrote about a while ago. We’ve called this Graphchain for the purposes of naming things. Then we will talk about the design choices, the main challenges, and then a conclusion.

Just in case you’re interested in where this came from, I originally wrote this paper — *Graphchain: a Blockchain-free Scalable Decentralised Ledger* — with Xavier Boyen and Thomas Haines, in 2016. We put this on ePrint and there’s a perhaps more readable version in an ERCIM News article. This work is also published in other places. but these are probably the easiest to find.

## What Are DAGs?

First, what do we mean by DAG? We mean a Directed Acyclic Graph. This sort of comes from this mathematical term for a graph, and generally you have these sets which consist of vertices and edges. Edges are just ordered pairs of vertices and they are normally represented as arrows if you have a directed graph. A graph is acyclic if you can’t start at one vertex and get back to the other following the arrows. You might understand that that is not exactly a mathematical term.

The diagram (below) is an example of a DAG. Edges — the arrows, and vertices — the orange boxes. You can see by inspection here that there are no cycles. You can’t start at one of these orange boxes, follow the arrows and get back to an orange box. That’s a DAG. You can also label these DAGs.

If you do, you can have what is called a Partially Ordered Set. In the work that we did, we talk a lot about Partially Ordered Sets. The idea here is you have a partial ordering because, if you define an arrow going to something as being higher than the one that the arrow is coming from, you can easily see that *k *is above all of these other letters. You can also quickly see that for *f *and *h, *there is no…