user2236: I've heard that the eUTxO model and the Account model are mathematically equivalent in terms of expressiveness in various YouTube videos. I've also heard that the eUTxO model is a strict superset of the Account model (ie: the eUTxO model can do everything the Account model can do, and more). Are these ideas/facts true? I've been trying to find a high quality source for this idea/fact but haven't been able to find one.
I tried reading the paper presenting the eUTxO model but my lack of formal math training made it a bit difficult and I didn't find any mentions of Account model equivalence.
Does anyone know of high quality sources which confirm or reject out these ideas?

user2236: I stumbled across this paper by IOHK which seems to show this sort of equivalence.
I'm going to try to read it and see what I can learn. I suspect this might be the best resource for learning about this mathematical equivalence between those two models.
EDIT: this seems like the paragraph from the paper above which confirms the idea that eUTxO is a mathematical superset of the account model:

Despite the accounting equivalence implied by the
translations, Proposition 2 and the translation of Sec.
5.2 show that it is generally necessary to create several
account-based transactions to simulate the effect of
a single UTXO-based transaction. This is important:
while all the value transfers in a single UTXO-based
transaction are processed atomically and simultaneously, the corresponding account-based transactions
are not guaranteed to be so. Theoretically, there may
be a wide time gap between their executions.


user4302: The reason eUTXO is considered a superset of the account model is because it is possible to create constraint emitting machines (CEMs) on the eUTXO model, as mentioned in the paper you linked. To summarize:
Since "smart contract" logic is encapsulated entirely within individual UTXO(s), it is possible to perfectly capture logic of arbitrary complexity by aggregating and quarantining UTXOs into a sort of "black box" on-chain.
It is this CEM principle that forms the basis of the Hydra Head Protocol; allowing the creation of mini-ledgers that can be configured to behave in an account-style fashion, all while periodically committing snapshots to the overarching UTXO-style main-chain.
All of this is to say, that any and all UTXO logic can be expressed in an accounts-like fashion, but the reverse is not true. Therefore, the UTXO model is, expressively speaking, a superset of the account model.

2236: <p>I've heard that the eUTxO model and the Account model are mathematically equivalent in terms of expressiveness in various YouTube videos. I've also heard that the eUTxO model is a strict superset of the Account model (ie: the eUTxO model can do everything the Account model can do, and more). Are these ideas/facts true? I've been trying to find a high quality source for this idea/fact but haven't been able to find one.</p>
<p>I tried reading the <a href="https://iohk.io/en/research/library/papers/the-extended-utxo-model/" rel="nofollow noreferrer">paper presenting the eUTxO model</a> but my lack of formal math training made it a bit difficult and I didn't find any mentions of Account model equivalence.</p>
<p>Does anyone know of high quality sources which confirm or reject out these ideas?</p>
 2236: <p>I stumbled across <a href="https://iohk.io/en/research/library/papers/chimeric-ledgerstranslating-and-unifying-utxo-based-and-account-based-cryptocurrencies/" rel="nofollow noreferrer">this paper</a> by IOHK which seems to show this sort of equivalence.</p>
<p>I'm going to try to read it and see what I can learn. I suspect this might be the best resource for learning about this mathematical equivalence between those two models.</p>
<p>EDIT: this seems like the paragraph from the paper above which confirms the idea that eUTxO is a mathematical superset of the account model:</p>
<blockquote>
<p>Despite the accounting equivalence implied by the
translations, Proposition 2 and the translation of Sec.
5.2 show that it is generally necessary to create several
account-based transactions to simulate the effect of
a single UTXO-based transaction. This is important:
while all the value transfers in a single UTXO-based
transaction are processed atomically and simultaneously, the corresponding account-based transactions
are not guaranteed to be so. Theoretically, there may
be a wide time gap between their executions.</p>
</blockquote>
 4302: <p>The reason eUTXO is considered a superset of the account model is because it is possible to create constraint emitting machines (CEMs) on the eUTXO model, as mentioned in the paper you linked. To summarize:</p>
<p><strong>Since &quot;smart contract&quot; logic is encapsulated <em>entirely</em> within individual UTXO(s), it is possible to <em>perfectly</em> capture logic of arbitrary complexity by aggregating and quarantining UTXOs into a sort of &quot;black box&quot; on-chain.</strong></p>
<p>It is this CEM principle that forms the basis of the <a href="https://eprint.iacr.org/2020/299.pdf" rel="nofollow noreferrer">Hydra Head Protocol</a>; allowing the creation of mini-ledgers that can be configured to behave in an account-style fashion, all while periodically committing snapshots to the overarching UTXO-style main-chain.</p>
<p>All of this is to say, that <strong>any and all UTXO logic can be expressed in an accounts-like fashion, but <em>the reverse is not true</em></strong>. Therefore, the UTXO model is, expressively speaking, a superset of the account model.</p>
