Abstract

One of the most simple models of computation suitable for representation of reactive systems behavior is a finite state transducer that operates on an input alphabet of control signals and an output alphabet of basic actions. The behavior of such a reactive system displays itself in the correspondence between the flow of control signals and sequence of basic actions performed by the system. We believe that the behavior of this kind requires more complex and expressive means of specifications than the conventional linear temporal logic (\(LTL\)). In this paper, we define a new language of formal specifications \(\mathcal{L}\mathcal{P}\)-\(LTL\), which is an extension of LTL, specifically intended for describing the properties of transducer computations. In this extension, the temporal operators are parameterized by sets of words (languages) which describe flows of control signals that impact on a reactive system. Basic predicates in the ℒ𝒫-LTL formulas are also defined by the languages in the alphabet of basic actions; these languages describe the expected response of the system to the environmental influences. In our earlier papers, we considered a verification problem for finite state transducers with regard to specifications represented by the ℒ𝒫-\(LTL\) and ℒ𝒫-\(CTL\) formulas. It was shown that the problem is algorithmically solvable for both logics. The aim of this paper is to estimate the expressive power of ℒ𝒫-\(LTL\) by comparing it with some well-known logics widely used in computer science for specification of reactive systems. Two fragments were isolated in the ℒ𝒫-LTL: ℒ𝒫-1-LTL and ℒ𝒫-n-LTL. We discovered that the specification language of ℒ𝒫-1-\(LTL\) is more expressive than LTL, while the ℒ𝒫-n-\(LTL\) fragment has the same expressive power as the monadic second order logic S1S.

Keywords:

temporal logics, expressive power, specification, verification, Büchi automata, infinite words

中文翻译：

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关于线性时间逻辑的某些扩展的表达能力

摘要

适用于表示无功系统行为的最简单的计算模型之一是有限状态换能器，其在控制信号的输入字母和基本动作的输出字母上运行。这种无功系统的行为在控制信号流与系统执行的基本动作序列之间的对应关系中显示出来。我们认为，这种行为比常规的线性时间逻辑（\（LTL \））需要更复杂和更具表现力的规范手段。在本文中，我们定义了形式规范\（\ mathcal {L} \ mathcal {P} \） - \（LTL \）的新语言，它是LTL的扩展，专门用于描述换能器计算的属性。在此扩展中，时间运算符通过描述影响无功系统的控制信号流的单词（语言）集进行参数化。L -LTL公式中的基本谓词也由基本动作字母中的语言定义；这些语言描述了系统对环境影响的预期响应。在我们的早期论文中，我们考虑了由state- \（LTL \）和ℒ𝒫- \（CTL \）公式表示的规格的有限状态传感器的验证问题。结果表明，该问题对于两种逻辑都是算法可解决的。本文的目的是评估ℒ𝒫-的表达能力。\（LTL \）通过将其与一些知名逻辑广泛应用于计算机科学反应系统的规格进行比较。两个片段隔离在ℒ𝒫 -LTL：ℒ𝒫 - 1- LTL和ℒ𝒫 -n-LTL。我们发现ℒ𝒫-1- \（LTL \）的规范语言比LTL更具表现力，而ℒ𝒫- n - \（LTL \）片段具有与一阶二阶逻辑S1S相同的表现力。

关键字：

时间逻辑，表达能力，规范，验证，Büchi自动机，无限词