  In 2013 Bei, Chen and Zhang introduced a trial and error model of computing,
and applied to some constraint satisfaction problems. In this model the input
is hidden by an oracle which, for a candidate assignment, reveals some
information about a violated constraint if the assignment is not satisfying. In
this paper we initiate a {\em systematic} study of constraint satisfaction
problems in the trial and error model. To achieve this, we first adopt a formal
framework for CSPs, and based on this framework we define several types of
revealing oracles. Our main contribution is to develop a \emph{transfer
theorem} for each type of the revealing oracle, under a broad class of
parameters. To any hidden CSP with a specific type of revealing oracle, the
transfer theorem associates another, potentially harder CSP in the normal
setting, such that their complexities are polynomial time equivalent. This in
principle transfers the study of a large class of hidden CSPs, possibly with a
promise on the instances, to the study of CSPs in the normal setting. We then
apply the transfer theorems to get polynomial-time algorithms or hardness
results for hidden CSPs, including satisfaction problems, monotone graph
properties, isomorphism problems, and the exact version of the Unique Games
problem. Most of the proofs of these results are short and straightforward,
which exhibits the power of the transfer theorems.
