🤖 AI Summary
This work addresses the satisfiability checking problem for transcendental functions in Nonlinear Real Arithmetic (NRA). Traditional approaches struggle to simultaneously achieve high precision, computational efficiency, and independent verifiability. We propose a novel, formally verifiable numerical certificate framework that models transcendental constraint solving as an explicit certificate search problem with guaranteed precision. Our method integrates adaptive floating-point arithmetic, interval Newton methods, symbolic-numeric hybrid verification, and backward error analysis. The resulting certificates are independently verifiable by third parties in sub-second time, with negligible failure probability. Experimental evaluation on multiple benchmarks demonstrates high-precision satisfiability determination, overcoming the inherent accuracy-efficiency trade-off that limits pure symbolic reasoning and classical interval analysis.
