A Lattice-Theoretic Formulation for Rate Monotonic Schedulability Analysis

Fixed-priority schedulability analysis for uniprocessor real-time systems is computationally difficult, and exact Rate Monotonic (RM) analysis is weakly NP-complete. This paper develops an exact lattice-theoretic formulation for the family of weighted feasibility problems induced by the exact RM schedulability test. For each candidate period, the corresponding weighted feasibility instance is mapped to a lattice embedding in which feasible values correspond to unique canonical lattice vectors, feasibility is characterized exactly by membership in an explicit constrained region, and candidate interactions satisfy exact carry/borrow correction identities. A determinant-based normalization of the embedding scale is also derived. The results provide an exact structural description of the RM weighted feasibility family together with an empirically informative candidate mechanism.