Pushout Attachments and Conditional Complexity of Executable Models

Abstract

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.