可执行模型的推出连接与条件复杂性
Pushout Attachments and Conditional Complexity of Executable Models
AI总结：
本文通过推出构造研究可执行模型的模块化扩展，提出语义判据和复杂性界限，区分语法与语义，揭示模块化偏好源于连接限制。
AI中文摘要：
我们通过有限带类型表示的推出（pushout）来表示可执行模型的模块化扩展。粘附性（adhesivity）保持了原始模型并恢复了共享接口，而选定的推出使得连接具有函子性，余积（coproducts）描述了并行连接。语义比较为行为持续性提供了精确的判据。有效连接还限定了条件前缀复杂性；在所述的规范化和不变性假设下，连接和扩展编码在加性常数范围内产生相同的损失对复杂性的分布，并共享一个精确的标量包络。该结果区分了语法、语义、理想复杂性和具体编码成本，并表明对模块化的偏好只能通过对允许连接的约束而产生。
英文摘要：
We represent the modular enlargement of an executable model by a pushout of finite typed presentations. Adhesivity preserves the original model and recovers the shared interface, while chosen pushouts make linking functorial and coproducts describe parallel attachments. A semantic comparison gives a precise criterion for behavioral persistence. Effective linking also bounds conditional prefix complexity; under the stated canonicalization and invariance assumptions, attachment and extension codes yield the same profiles of loss against complexity, up to additive constants, and share an exact scalar envelope. The result separates syntax, semantics, ideal complexity, and concrete coding cost, and shows that a preference for modularity can arise only through restrictions on the permitted attachments.
