MCSAT Modulo Transcendental Arithmetics

2026-05-30

AI Summary

This work addresses the undecidable satisfiability problem for nonlinear real arithmetic formulas involving transcendental functions such as exponentials and trigonometric functions. It presents the first extension of the MCSAT framework to transcendental real arithmetic by introducing a mediator plugin mechanism that abstracts the original formula into a nonlinear real arithmetic (NRA) problem. The approach integrates an NRA solver with real analytic methods, dynamically maintaining abstraction consistency and iteratively refining the model during search. Implemented in Yices2 with support for sine and exponential functions, the method demonstrates superior performance over state-of-the-art solvers on both satisfiable and unsatisfiable benchmarks.

Abstract

We propose a framework for solving quantifier-free formulas from (undecidable) extensions of non-linear real arithmetic (NRA) with transcendental functions, such as exponential and trigonometric ones. The framework extends the Model Constructive Satisfiability calculus (MCSAT), and leverages procedures for NRA and methods from real analysis. At its core, our procedure abstracts the input formula to NRA, and lets MCSAT and an NRA plugin incrementally build a partial model of the abstracted formula. A Transcendental Real Arithmetic plugin, acting as an intermediary between MCSAT and the NRA plugin, ensures the consistency of the partial model and is responsible for refining the abstracted formula. We implemented our procedure in the Yices2 SMT solver for the sine and exponential functions, and conducted an extensive empirical evaluation that shows that our prototype outperforms state-of-the-art solvers on both SAT and UNSAT instances.

Problem

• Satisfiability Modulo Theories
• Non-linear Real Arithmetic
• Transcendental Functions
• MCSAT

Innovation

• MCSAT
• transcendental functions
• non-linear real arithmetic
• SMT solving
• model construction