In the last decades much research effort has been devoted to extending the success of model checking from the traditional field of finite state machines and various versions of temporal logics to suitable subclasses of context-free languages and appropriate extensions of temporal logics. To the best of our knowledge such attempts only covered structured languages, i.e. languages whose structure is immediately “visible” in their sentences, such as tree-languages or visibly pushdown ones. In this paper we present a new temporal logic suitable to express and automatically verify properties of operator precedence languages. This “historical” language family has been recently proved to enjoy fundamental algebraic and logic properties that make it suitable for model checking applications yet breaking the barrier of visible-structure languages (in fact the original motivation of its inventor Floyd was just to support efficient parsing, i.e. building the “hidden syntax tree” of language sentences). We prove that our logic is at least as expressive as analogous logics defined for visible pushdown languages yet covering a much more powerful family; we design a procedure that, given a formula in our logic builds an automaton recognizing the sentences satisfying the formula, whose size is at most exponential in the length of the formula. Our results cover both finite and infinite string languages.

在过去的几十年中，已经进行了许多研究工作，以将模型检查的成功从有限状态机的传统领域和时态逻辑的各种版本扩展到上下文无关语言的适当子类以及时态逻辑的适当扩展。据我们所知，这种尝试仅覆盖结构化语言，即结构在其句子中立即“可见”的语言，例如树状语言或明显下推式语言。在本文中，我们提出了一种新的时态逻辑，适用于表达和自动验证运算符优先级语言的属性。该“历史”语言家族最近被证明具有基本的代数和逻辑特性，使其适合于模型检查应用程序，但打破了可见结构语言的障碍（事实上，其发明者Floyd的最初动机只是为了支持有效的解析），即建立语言句子的“隐藏语法树”。我们证明了我们的逻辑至少与为可见下推式语言定义的类似逻辑一样具有表现力，但涵盖了更强大的系列。我们设计了一个过程，给定逻辑中的公式，该程序将构建一个自动机，以识别满足该公式的句子，该句子的大小最多为公式长度的指数。我们的结果涵盖了有限和无限字符串语言。