This paper presents a complete constructive framework for solving specific subclasses of exponential Diophantine equations through hierarchical differential algebraic methods. Unlike previous non-constructive approaches, we provide explicit computational procedures with rigorous error bounds for equations satisfying certain structural conditions. Our key contributions include: (1) Constructive definitions avoiding transfinite recursion for well-conditioned systems; (2) Explicit solution formulas with computable basis functions and coefficient polynomials for equations with dominant monomial structure; (3) Complete numerical analysis with proven error bounds under appropriate regularity conditions; (4) Experimental validation demonstrating high-precision accuracy (residuals < 10−20) for structured problem classes; (5) Rigorous reconciliation with classical impossibility results. The framework achieves polynomial complexity for systems with low treewidth and symmetry, while honestly acknowledging the fundamental limitations imposed by undecidability results.
liu et al. (Sat,) studied this question.