TensorEQC: Structure-Aware Equivalence Checking with GF(2) Algebra, Exact Tensor Networks, and Reset Analysis : a Multi-Algorithmic Study of Datapath Verification and Reset-State Dependence

Abstract Equivalence checking is sensitive to the representation of a circuit. XOR-rich networks, carry chains, finite-field multipliers, and integer multipliers expose different kinds of exact structure. We describe TensorEQC, an executable research workflow combining structural hashing, counterexample simulation, algebraic normal forms over GF(2), relational tensor-network elimination, ordered binary decision diagrams, and small-support exhaustive evaluation. A companion module checks reset dependence by explicit-state self-composition; exact tensor-train tools measure algebraic rank and test zero functions. The reported synthetic campaign includes 2,048-bit rewritten ripple adders and 128-bit polynomial-basis multipliers, as well as cases where the portfolio adds overhead or reaches its limits. A supplementary experiment performed for this manuscript reconstructs five complete 16-input functions from exact GF(2) tensor trains, validates all unfolding ranks, and checks a parity-cancellation negative control. The results support structure-dependent engine selection, not universal tensor superiority. Timing comparisons are against internal baseline engines, not commercial or SAT-based systems. The submission distinguishes newly reproduced evidence from previously reported campaign results whose original execution artifacts must accompany an archival release.