Search Strategy for Exhaustive Generation of Parameter Settings for a Student Model

ASPM Analysis of Symbolic Parameter Models] is a powerful tool for the analysis of discrete parameter cognitive models. However, it requires that the model generate as output the responses for all possible combinations of parameter settings, for a given task. For the domain of student modelling the runtimes associated with generating such outputs are exponential in the number of parameters. This leads to a combinatorial explosion which has to be contained in order to perform realistic modelling tasks. We used a student diagnosis program called DEBUGGY, which diagnoses subtraction skills, as a reference and designed a student modelling program called DEB which functions as a front end to ASPM. To contain the combinatorics of the task we had to cut down the exploration of the search space, for which we developed a notion of state that is valid for all discrete parameter models that exhaustively enumerate all parameterizations. We present a search strategy that successfully reduces the state space searched. A search space pruning algorithm which saves states of the search space and matches newly generated states with earlier states was implemented and tested. The states are matched using a general matching criterion developed for cognitive models which share common features with DEB. Our approach avoids redundant search and yet does not compromise the integrity of the solution generation. The algorithm and its development are described and alternative approaches are compared. We also suggest some techniques which we believe will lead to further improvement in the eeciency of the search.