Complexity verification using guided theorem enumeration

Akhilesh Srikanth, Burak Sahin, William R. Harris
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引用次数: 23

Abstract

Determining if a given program satisfies a given bound on the amount of resources that it may use is a fundamental problem with critical practical applications. Conventional automatic verifiers for safety properties cannot be applied to address this problem directly because such verifiers target properties expressed in decidable theories; however, many practical bounds are expressed in nonlinear theories, which are undecidable. In this work, we introduce an automatic verification algorithm, CAMPY, that determines if a given program P satisfies a given resource bound B, which may be expressed using polynomial, exponential, and logarithmic terms. The key technical contribution behind our verifier is an interpolating theorem prover for non-linear theories that lazily learns a sufficiently accurate approximation of non-linear theories by selectively grounding theorems of the nonlinear theory that are relevant to proving that P satisfies B. To evaluate CAMPY, we implemented it to target Java Virtual Machine bytecode. We applied CAMPY to verify that over 20 solutions submitted for programming problems hosted on popular online coding platforms satisfy or do not satisfy expected complexity bounds.
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使用引导定理枚举的复杂度验证
确定给定程序是否满足其可能使用的资源量的给定界限是关键实际应用中的一个基本问题。传统的安全属性自动验证器不能直接用于解决这一问题,因为此类验证器的目标是用可确定的理论表示的属性;然而,许多实际边界是用非线性理论表示的,这是不可确定的。在这项工作中,我们引入了一种自动验证算法CAMPY,它确定给定的程序P是否满足给定的资源界B,该资源界B可以用多项式,指数和对数项表示。我们的验证器背后的关键技术贡献是非线性理论的插值定理证明器,它通过选择性地建立与证明P满足b相关的非线性理论定理,惰性地学习非线性理论的足够精确的近似值。为了评估CAMPY,我们将其实现为Java虚拟机字节码。我们应用CAMPY验证了在流行的在线编码平台上托管的编程问题提交的20多个解决方案满足或不满足预期的复杂性界限。
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