发表机构
United Arab Emirates University; Abu Dhabi Polytechnic（阿联酋大学; 阿布扎比理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出课程计划语言的形式模型，证明学位时间与学分负担的复杂性来源不同，并基于22所大学语料库验证容量是主要约束。
AI 中文摘要
我们将学术课程建模为可行学习计划语言的生成器：先修课程是合取范式中的单调布尔公式，学位要求是学分阈值覆盖约束，学习计划是受每学期学分容量限制的学期序列。在该模型中，我们解决了两个自然规划目标的复杂性，即获得学位的学期数和总学分负担，并隔离了导致每种困难的结构性承诺。当每学期容量无界时，获得学位的时间是多项式的，适用于任意析取先修课程和任意选修课，因此析取永远不会导致其困难性，但一旦容量受限，即使没有任何先修课程，它也会变得强NP难。负担是互补的：析取和重叠选修课各自在孤立情况下都是强NP难的，且其复杂性不依赖于容量，而负担在合取、必修部分上是多项式的。因此，这两个目标具有不相交的困难来源。我们证明了标准课程复杂性度量的延迟因子分量是获得学位时间的多项式可计算上界，在合取部分上是精确的，在其他地方则宽松，其差值我们命名为析取松弛，并证明了课程子sumption是coNP完全的，共识先修课程恢复是NP完全的。在二十二所大学的语料库上实例化该模型，我们发现88%的带先修课程的课程是纯合取的，且容量而非先修逻辑是获得学位时间的有效约束。课程语料库可公开获取（此https URL），分析和图形生成代码随论文提供。
英文摘要
We model an academic curriculum as a generator of a language of feasible study plans: prerequisites are monotone Boolean formulas in conjunctive normal form, degree requirements are credit-threshold covering constraints, and a study plan is a sequence of terms bounded by a per-term credit capacity. Within this model, we settle the complexity of the two natural planning objectives, the number of terms to a degree and the total credit load, and we isolate the structural commitment responsible for each source of hardness. Time to degree is polynomial whenever the per-term capacity is unbounded, for arbitrary disjunctive prerequisites and arbitrary electives, so disjunction never contributes to its hardness, yet it becomes strongly NP-hard as soon as capacity binds, even without any prerequisite. Load is complementary: disjunction and overlapping electives are each strongly NP-hard in isolation and their complexity does not depend on capacity, while load is polynomial on the conjunctive, mandatory fragment. The two objectives therefore have disjoint sources of hardness. We show that the delay-factor component of the standard curricular-complexity metric is a polynomially computable upper bound on time to degree, exact on the conjunctive fragment and loose elsewhere by a quantity we name the disjunctive slack, and we prove that program subsumption is coNP-complete and consensus prerequisite recovery is NP-complete. Instantiating the model on a corpus of twenty-two universities, we find that 88 percent of prerequisite-bearing courses are purely conjunctive and that capacity, not prerequisite logic, is the operative constraint on time to degree. The curriculum corpus is openly available (https://doi.org/10.5281/zenodo.22334674), and the analysis and figure-generation code accompany the paper.
Comments17 pages, 2 figures, 2 tables
