A Practical Approximation to the Halting Problem using Iterative Bi-Directional Quantum-AI Algorithms

This research introduces an approximate, evolution-based framework aimed at addressing the Halting Problem in a practical and non-deterministic manner. While the Halting Problem remains mathematically undecidable, this work proposes a bidirectional evolutionary cycle that iterates from start-to-end and then from end-to-start, with a central evaluation point acting as a stability reference (similar to a clock returning to 12). The model integrates adaptive evolution, self-correction, and pattern recognition to approximate program-halting behavior with improved reliability over traditional heuristic methods. To enhance predictive capability, the framework is designed for integration with quantum-assisted computation and advanced AI models, enabling deeper analysis of execution paths and reducing uncertainty across iterative cycles. This approach does not claim to solve the Halting Problem but instead provides a structured, practical, and computationally scalable method for estimating halting behavior under real-world constraints. The proposed model opens the door for further research in hybrid quantum–AI reasoning systems, self-evolving algorithms, and approximation-driven logic analysis