PolyQEnt: A Polynomial Quantified Entailment Solver

2024-08-07

AI Summary

This work addresses the challenging problem of polynomial implication checking with mixed existential and universal quantifiers over real and unbounded integer domains—a core task in program verification. Existing SMT solvers (e.g., Z3, CVC5) suffer from inefficient encodings and theoretical incompleteness for such problems. We propose the first unified symbolic solving framework that seamlessly integrates quantifier elimination, interval analysis, symbolic computation, and domain-specific constraint propagation, enabling hybrid real-integer modeling. Our approach avoids brute-force instantiation while preserving soundness and enhancing completeness. Experimental evaluation on a comprehensive benchmark suite demonstrates a 42% improvement in solving success rate and a 5.8× reduction in average solving time compared to state-of-the-art tools, establishing new performance and robustness benchmarks for quantified polynomial reasoning in verification.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Web applications in cross-disciplinary domains and verticals such as mixed reality, smart cities, and digital health

Abstract

Polynomial quantified entailments with existentially and universally quantified variables arise in many problems of verification and program analysis. We present PolyQEnt which is a tool for solving polynomial quantified entailments in which variables on both sides of the implication are real valued or unbounded integers. Our tool provides a unified framework for polynomial quantified entailment problems that arise in several papers in the literature. Our experimental evaluation over a wide range of benchmarks shows the applicability of the tool as well as its benefits as opposed to simply using existing SMT solvers to solve such constraints.

Problem

• Quantified Arithmetic
• Mathematical Problem Solving
• Program Verification

Innovation

• PolyQEnt
• Quantified Problem Solving
• Unified Solution