Semidefinite programming for the educational testing problem
Methods for solving the educational testing problem which arises from statistics are considered. The problem is to find lower bounds for the reliability of the total score on a test (or subtests) whose items are not parallel using data from a single test administration. We formulate the problem as an optimization problem with a linear objective function and semidefinite constraints. We maintain exact primal and dual feasibility during the course of the algorithm. The search direction is found using an inexact Gauss–Newton method rather than a Newton method on a symmetrized system. Computational results illustrating the robustness of the algorithm are successfully exploited.
We continue the study of bottom-up unranked tree automata with equality and ::: disequality constraints between direct subtrees. In particular, we show that ::: the emptiness problem for the nondeterministic automata is decidable. In ::: addition, we show that the universality problem, in contrast, is undecidable.