EOS uses a BFT consensus algorithm, so, by default, all nodes (producing and non-producing) validate and process all transactions and blocks to compute the state at each timestep.
However, in the whitepaper, there is a mention of an optional "Partial Evaluation of Blockchain State":
Partial Evaluation of Blockchain State
Scaling blockchain technology necessitates that components are
modular. Everyone should not have to run everything, especially if
they only need to use a small subset of the applications.
An exchange application developer runs full nodes for the purpose of
displaying the exchange state to its users. This exchange application
has no need for the state associated with social media applications.
EOS.IO software allows any full node to pick any subset of
applications to run. Actions delivered to other applications are
safely ignored if your application never depends upon the state of