The only substantive issue I disagree with is Peter's claim that brains are not parallel processors - I think he is arguing for this point beyond merely conflating parallel processors with massively parallel computing.
Another generalization is to solve the problem when many parallel processors are available. In this case, instead of adding the costs of computing each subsequence, we just take the maximum, because we can do them both simultaneously.
In other words, a problem A is in P-complete if, for each problem B in P, there are constants c and k such that B can be reduced to A in time O((log n)c) using O(nk) parallel processors. See NC for the definition of parallel processors.
 See also: Pattern recognition, Ancestor
  
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