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At first glance, dreaming may seem less like computation than any other activity of the human mind. The impressive achievements of artificial intelligence research (Boden, 1977; Dennett, 1978; Simon, 1981) have shown that computers, when expertly programmed, can perform in a way that closely resembles rational thoughts in humans. But dreaming has always been the exception to the rule of reason in mental life. The dream has been seen as the medium of the irrational, of the wild and willful elements in human nature, if not of a supernatural intrusion into the human world. Subjective experience tends to confirm these primitive impressions. To the dreamer, dreaming seems not only disorderly but defiantly so.
Psychoanalysis, of course, has mitigated this extreme view. It has demonstrated that beneath the apparent defiance of order, dreaming is both meaningful and motivated. However, the traditional psychoanalytic theory of dream construction does not locate these elements of meaning and motivation in the actual content of the dream, but in the dreamer's associations. For the traditional theory (Freud, 1900, 1917), the manifest content is an unstructured conglomerate of disconnected fragments, accidentally thrown together by the thrust of irrational forces.
Meaningful and motivated mental activity is by nature computational. Even the expression of the most primitive impulse requires the matching of an inner mental schema of the desired object with the real objects actually available in the outside world. The matching process itself, even at so simple a level, is a form of computation (Palombo, 1980).
The short answer to my question is therefore that all of our dreaming is done by computer, the same biological computer that does the rest