A challenging problem for autonomous systems is to synthesize a reactive controller that conforms to a set of given correctness properties. Linear temporal logic (LTL) provides a formal language to specify the desired behavioral properties of systems. In applications in which the specifications originate from various aspects of the system design, or consist of a large set of formulas, the overall system specification may be unrealizable. Driven by this fact, we develop an optimization variant of synthesis from LTL formulas, where the goal is to design a controller that satisfies a set of hard specifications and minimally violates a set of soft specifications. To that end, we introduce a value function that, by exploiting the LTL semantics, quantifies the level of violation of properties. Inspired by the idea of bounded synthesis, we fix a bound on the implementation size and search for an implementation that is optimal with respect to the said value function. We propose a novel maximum satisfiability encoding of the search for an optimal implementation (within the given bound on the implementation size). We iteratively increase the bound on the implementation size until a termination criterion, such as a threshold over the value function, is met.

中文翻译：

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具有最大可实现性的线性时序逻辑规范的反应式综合

自治系统的一个具有挑战性的问题是合成一个符合一组给定正确性属性的反应控制器。线性时序逻辑 (LTL) 提供了一种形式语言来指定系统所需的行为属性。在规范源自系统设计的各个方面或由大量公式组成的应用中，整个系统规范可能无法实现。在这一事实的推动下，我们从 LTL 公式开发了一种合成的优化变体，其目标是设计一个满足一组硬规范并最小化违反一组软规范的控制器。为此，我们引入了一个价值函数，通过利用 LTL 语义，量化违反属性的程度。受有界综合思想的启发，我们确定实现大小的界限，并搜索相对于所述价值函数最佳的实现。我们提出了一种新颖的最大可满足性编码，以寻找最佳实现（在实现大小的给定范围内）。我们迭代地增加实现大小的界限，直到满足终止标准，例如值函数上的阈值。