Instructional Sequencing Over Prerequisite DAGs: Stochasticity Collapses, NP-Hardness Persists

A recent paper in theoretical computer science, available on arXiv (ID 2608.05455), explores the complexities involved in instructional sequencing, where students learn concepts linked by prerequisite relationships. The authors frame this issue as a stochastic shortest-path problem, where the probability of successfully grasping a concept depends on the learner's current state, and failure does not alter that state. They demonstrate that this stochastic aspect can be precisely eliminated, simplifying the problem to a deterministic shortest-path scenario on the lattice of prerequisite order ideals, while maintaining optimal values and actions. However, while stochastic complexity is removed, combinatorial complexity persists: optimal sequencing is NP-hard, even under strict conditions—such as no prerequisite edges and uniform binary nonnegative transfer with success probabilities of at least 1/2. This difficulty is shown through a reduction from the feedback arc set problem in tournaments. Interestingly, the problem can become manageable when transfer preferences are jointly acyclic under specific conditions. This research, announced on August 26, 2025, contributes to the field of educational technology and adaptive learning systems, emphasizing the challenges of optimizing instructional sequences, even in simplified scenarios.