The Roles of Internal Representation and Processing in Problem Solving Involving Insight: A Computational Complexity Perspective

In human problem solving, there is a wide variation between individuals in problem solution time and success rate, regardless of whether or not this problem solving involves insight. In this paper, we apply computational and parameterized analysis to a plausible formalization of extended representation change theory (eRCT), an integration of problem solving by problem space search and insight as problem restructuring which proposes that this variation may be explainable by individuals having different problem representations and search heuristic choices. Our analyses establish not only the intractability of eRCT in general, but also sets of restrictions under which eRCT-based problem solving can and cannot be done quickly. As such, our analyses both prove that several conjectures about what makes problem solving under eRCT possible in practice are incomplete, in the sense that not all factors in the model whose restriction is responsible for efficient solvability are part of the explanation, and provide several new explanations that are complete.