Complexity class associated with exhaustive search What is the complexity class associated with exhaustive search algorithms? (if there is one)

Is it NP or PSPACE?

Are there restricted models of computation capturing the class of exhaustive search algorithms similar to models for greedy and dynamic programming?
It's a little vague, but I like the question. I wrote a paper about it a LONG time ago. 
Maybe this will help the Anonymous questioner: 

Brute Force Search and Oracle-Based Computation 

Here's a summary. Informally, if you do not keep any scratch work from previous trials, and just try all possible solutions in lexicographical order until a desired solution is found, then brute force corresponds precisely to $P^{NP}$. If you keep around even $3$ bits of scratch work from one possible solution to the next, then you can do $PSPACE$, via Barrington's theorem. There are other possibilities, such as what happens when you don't run in lex order but according to some other efficiently computable list of all strings.

[WARNING WARNING WARNING: It's likely that I disagree with almost all opinions stated in this paper. It was written about 10 years ago, by someone with the same name but who is essentially a different person.]