Mathematical detail alone does not dictate hardware cost. Instead, resource demands are driven entirely by operationally distinguishable future behaviors. This paper introduces a task-semantic framework that groups identical behavioral behaviors into distinct classes. The total number of these classes defines the absolute minimum number of abstract states any valid system must maintain, establishing a strict floor for required memory bits. The framework models specification updates as partition refinements. While refining a specification can increase the number of required behavioral classes, it does not automatically guarantee higher engineering costs. This distinction leaves room for efficiency strategies like data compression or recomputation. For approximate designs, the framework swaps exact state counting for metric separation. It uses packing numbers to define impossibility boundaries for a given error threshold, and covering numbers to map out a continuous approximation frontier. Ultimately, it offers a modular methodology that translates behavioral semantics into hardware-specific resource bounds. ( direct link )