General description of PoW blockchain algorithm?

Question

bitcoin

can the chain of blocks be considered as an acyclic graph?
where, in order to add the next node (block), it is necessary to solve some computationally complex problem, which can be written in general form as follows . It is
necessary to choose a value of x that satisfies:
H(x) ≤y, where y is some fixed number.
for bitcoin, this formula seems to be suitable:
SHA256(SHA256(H)) < targethash , sorting through the nonce values, you need to choose such a header to fulfill this condition.
for Ethereum too:
PoW(Hn, nrand ,d) ≤2^256/H_d
what about other PoW algorithms? do they fit that description?

Answer 1

In general, yes. Only there are much more variables than just a nonce. And the set of transactions is constantly changing, both nTime and extraNonce.
PoW algorithms are usually similar to each other. Just a task that cannot be solved more optimally than by brute force. Required to prove the work expended.