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Efficient Interpolant Generation in Satisfiability Modulo Linear Integer Arithmetic

机译:可满足性模数线性整数算法中的有效插值生成

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The problem of computing Craig interpolants in SAT and SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of interest —including that of equality and uninterpreted functions (EUJ-), linear arithmetic over the rationals (£A(Q)), and their combination— and they are successfully used within model checking tools. For the theory of linear arithmetic over the integers (£A(Z)), however, the problem of finding an interpolant is more challenging, and the task of developing efficient interpolant generators for the full theory £A(Z) is still the objective of ongoing research. In this paper we try to close this gap. We build on previous work and present a novel interpolation algorithm for SMT(£A(Z)), which exploits the full power of current state-of-the-art SMT(£A(Z)) solvers. We demonstrate the potential of our approach with an extensive experimental evaluation of our implementation of the proposed algorithm in the MathS AT SMT solver.
机译:最近,在SAT和SMT中计算Craig插值的问题引起了人们的极大兴趣,主要是因为其在形式验证中的应用。对于一些有趣的理论,已经提出了有效的内插生成算法,包括等式和未解释函数(EUJ-),有理数上的线性算术(£A(Q))以及它们的组合,并且已在模型中成功使用检查工具。然而,对于整数(£A(Z))上的线性算术理论,寻找插值问题更具挑战性,为整个理论£A(Z)开发有效的插值生成器仍然是我们的目标。正在进行的研究。在本文中,我们试图弥补这一差距。我们在先前工作的基础上,提出了一种新颖的SMT(£A(Z))插值算法,该算法可充分利用当前最先进的SMT(£A(Z))求解器的功能。我们通过对MathS AT SMT求解器中所提出算法的实现进行广泛的实验评估,证明了该方法的潜力。

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