This paper presents a framework to derive instantiation-based decision procedures for satisfiability of quantified formulas in first-order theories, including its correctness, implementation, and evaluation. Using this framework we derive decision procedures for linear real arithmetic and linear integer arithmetic formulas with one quantifier alternation. We discuss extensions of these techniques for handling mixed real and integer arithmetic, and to formulas with arbitrary quantifier alternations. For the latter, we use a novel strategy that handles quantified formulas that are not in prenex normal form, which has advantages with respect to existing approaches. All of these techniques can be integrated within the solving architecture used by typical SMT solvers. Experimental results on standardized benchmarks from model checking, static analysis, and synthesis show that our implementation in the SMT solver cvc4 outperforms existing tools for quantified linear arithmetic.

中文翻译：

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通过反例引导实例化求解量化线性算法

本文提出了一个框架，用于推导出一阶理论中量化公式可满足性的基于实例化的决策程序，包括其正确性、实现和评估。使用这个框架，我们推导出线性实数算术和线性整数算术公式的决策程序，其中一个量词交替。我们讨论了这些技术的扩展，用于处理混合实数和整数算术，以及具有任意量词交替的公式。对于后者，我们使用一种新颖的策略来处理非 prenex 范式的量化公式，这相对于现有方法具有优势。所有这些技术都可以集成到典型 SMT 求解器使用的求解架构中。来自模型检查、静态分析、