While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we introduce the logic rLTL which provides a means to formally reason about both correctness and robustness in system design. Furthermore, we identify a large fragment of rLTL for which the verification problem can be efficiently solved, i.e., verification can be done by using an automaton, recognizing the behaviors described by the rLTL formula $\varphi$, of size at most $\mathcal{O} \left( 3^{ |\varphi|} \right)$, where $|\varphi|$ is the length of $\varphi$. This result improves upon the previously known bound of $\mathcal{O}\left(5^{|\varphi|} \right)$ for rLTL verification and is closer to the LTL bound of $\mathcal{O}\left( 2^{|\varphi|} \right)$. The usefulness of this fragment is demonstrated by a number of case studies showing its practical significance in terms of expressiveness, the ability to describe robustness, and the fine-grained information that rLTL brings to the process of system verification. Moreover, these advantages come at a low computational overhead with respect to LTL verification.

中文翻译：

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正确还不够：使用健壮的线性时序逻辑进行有效验证

尽管形式化方法中的大多数方法都可以解决系统的正确性，但是确保鲁棒性仍然是一个挑战。在本文中，我们介绍了逻辑rLTL，该逻辑rLTL提供了一种形式化的方法来正式推理系统设计的正确性和鲁棒性。此外，我们确定了可以有效解决验证问题的较大的rLTL片段，即可以通过使用自动机来完成验证，从而认识到由rLTL公式$ \ varphi $描述的行为，其大小最大为$ \ mathcal {O} \ left（3 ^ {| \ varphi |} \ right）$，其中$ | \ varphi | $是$ \ varphi $的长度。此结果改进了先前用于rLTL验证的$ \ mathcal {O} \ left（5 ^ {| \ varphi |} \ right）$的边界，并且更接近$ \ mathcal {O} \ left（ 2 ^ {| \ varphi |} \ right）$。通过大量案例研究证明了此片段的实用性，这些案例表明了它在表达能力，描述健壮性的能力以及rLTL带给系统验证过程的细粒度信息方面的实际意义。此外，相对于LTL验证，这些优点的计算开销较低。