A Fresh Look at Best Inductive Loop Invariant Synthesis for Bit-Vector Relations

Synthesizing best inductive invariants (BII) is fundamental to program analysis and verification, yet existing approaches face significant efficiency challenges. We introduce a new formulation for the problem through the lens of mathematical optimization over quantified constraints in first-order theories. The formulation offers a constructive and operational perspective on the BII problem and opens new algorithmic avenues. Building on this formulation, we present two new algorithms for bit-vector programs: a strategically guided linear search that exploits the lattice structure and a bitwise greedy approach that resolves bound bits from high to low with a solver-call count linear in bit-width. We evaluate our approach on a comprehensive benchmark suite, demonstrating significant performance improvements over conventional methods based on symbolic abstraction and chaotic iteration. Experimental results demonstrate our approach solves up to 86% more benchmarks than baseline methods, with improved scaling in solver-call count for high bit-widths and improved verification effectiveness when integrated with k-induction.