CARS: A Constrained Autonomous Rule Synthesis Framework for Self-Generating Algorithmic Systems

Autonomous algorithm generation remains a fundamental challenge in adaptive computational systems. Existing approaches generally rely on externally defined objectives, predefined optimization functions, or task-specific reward mechanisms, which limit their ability to generate and regulate novel computational rules under unknown conditions. This paper introduces CARS (Constrained Autonomous Rule Synthesis), a general framework for autonomous generation of valid algorithmic structures through an internally regulated evolutionary process. The framework separates the system into three fundamental components: a rule generation layer, a constraint evaluation layer, and a recursive adaptation layer. Candidate computational rules are generated within a bounded functional space, evaluated through intrinsic structural constraints, and selectively retained through iterative feedback. Unlike traditional optimization-driven approaches, CARS does not require a fixed external objective function as the sole evolutionary driver. Instead, it utilizes a closed-loop mechanism in which generated structures, historical states, and constraint conditions jointly determine subsequent evolution. The framework emphasizes boundedness, reversibility, controllability, and structural consistency as fundamental requirements for autonomous algorithmic development. The proposed model provides a theoretical foundation for studying constrained self-evolving computational systems, where algorithmic structures may emerge, adapt, and stabilize through recursive internal regulation. CARS is presented as a conceptual framework and mathematical architecture for future investigation into autonomous computation, adaptive control systems, and artificial evolution.