Stochasticity Is Not the Hard Part: Reduction and Complexity in Instructional Sequencing over Prerequisite DAGs

arXiv cs.AIAugust 7, 2026en

arXiv:2608.05455v1 Announce Type: new Abstract: When a student must learn concepts connected by prerequisite dependencies, when does the order of instruction matter, and what does it cost to find the best one? We study instructional sequencing as a stochastic shortest-path problem in which attempting a concept succeeds with a state-dependent probability and failure leaves the learner state unchanged. We first prove that this stochasticity can be eliminated exactly: the problem collapses to a deterministic shortest-path problem on the lattice of prerequisite order ideals, preserving optimal values and actions. The collapse removes stochastic complexity but not combinatorial complexity: optima

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