A Computational Model of Tower of Hanoi Problem Solving

Abstract

The Tower of Hanoi (TOH) is a classic problem solving task. Over the past twenty years, it has found new applications in domains of cognition such as executive function, in special populations such as patients with frontal lobe lesions, and with new measurement technologies such as functional neuroimaging. The resulting explosion of new data has not been matched by new theoretical accounts and computational models. This dissertation describes a new model of TOH problem solving. The model is evaluated against behavioral measures of normal young adults, behavioral measures of patients with frontal lobe lesions, and neuroimaging measures of normal young adults. The main achievement is the first comprehensive account of the new data on TOH problem solving. Secondary achievements include new insights into the nature of goals; a new account of selection between competing alternatives; a new theory of the interaction between frontal and parietal areas that synthesizes existing theories of problem solving and executive function; a novel methodological focus on the design decisions that arise during model construction rather than numerically-valued free parameters; and additional support for the breadth claims of the 4CAPS cognitive architecture. This research sets the stage for future investigations of other populations such as young children, other tasks such as verbal fluency, other brain areas such as the temporal areas where declarative long-term memories reside, and other computational topics such as learning.