Visual search: complexity of positive vs negative search tasks Thinking about experiments where participants perform visual search tasks, I remember hearing in a Cog Psych lecture that if the instructions of the task were of the form "find the element that has property X", the participants would accomplish the task faster and with greater ease than when the instructions were of the form "find the element that does not have property Y". 

It was then discussed that this exemplifies one of the themes in cognitive psych: The cognitive processes handle positive information better than negative information. Is this positivity effect?

I wonder if there is something about the second task that is algorithmically more complex than the first. Would a computer show the same slow-down for these tasks? Anyone know of any research exploring this?
I would doubt that the effect you described is an example for the positivity effect, which is a form of attributional bias, rather than connected to basic perceptual phenomena. 

Instead I think that the experimental results you described can be explained by a priming effect. Priming describes the phenomenon that the exposure to one stimulus influences the processing of following stimuli. If the first stimulus shares perceptual, semantic, or conceptual similarities with the next stimulus, processing is enhanced (positive priming). If it provides conflicting information, processing can be depressed (negative priming). 

Would a computer show the same behavior for these tasks?

Attempts to explain (positive) priming effects usually discuss an activation of associated memory contents, which, in turn, lead to enhancements in the following processing steps.

Since memory access is often indeed a limiting factor of computer performance, priming effects can possibly observed with computers, too. Computer have different types of storage systems which differ in access speed (e.g., hard disc, RAM, cache). For instance, information that is (pre-)loaded into cache memory (which is limited) can be accessed faster than information that is stored on the hard disc. Since it is context dependent which information is in cache memory at a point in time (i.e., it depends on the things you are doing at the moment), memory contents connected to the things you do right now are probably accessed faster (because they are in the cache) than other memory contents, hence, a priming effect.