🤖 AI Summary
This study addresses the inexecutability of task abstractions caused by spatial layout constraints under fixed controllers. We propose an affine-constraint-based layout repair method that compiles task requirements into affine constraints and modifies only continuous coordinates, thereby preserving the original event logic and controller. Furthermore, we introduce a most-violated-row update algorithm coupled with a quadratic projection mechanism to decouple the representation layer from the optimizer, enabling conditional bounded certification. Experimental results demonstrate that the proposed approach successfully certifies all layouts across three tasks, with its effectiveness further validated through 300 paired rollback tests.
📝 Abstract
A task abstraction can specify the intended events while its spatial layout prevents a fixed agent and controller from completing them. Starting from a supplied structured task record, we compile whole-task tracking, clearance, and actuation requirements into auditable affine layout constraints. We repair only declared continuous coordinates, preserving event order, timing, topology, and the controller. A most-violated-row update admits conditional finite-certification and net-displacement bounds; a same-compiler quadratic projection separates the representation from the optimizer. On three researcher-authored task abstractions, both backends certify all three layouts and complete all 300 fresh paired rollouts per backend. A risk-target sweep also exposes fixed event tests that the chosen certificate cannot satisfy through layout edits alone.