Weight monitoring with linear temporal logic: complexity and decidability

C. Baier, Joachim Klein, Sascha Klüppelholz, Sascha Wunderlich
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引用次数: 29

Abstract

Many important performance and reliability measures can be formalized as the accumulated values of weight functions. In this paper, we introduce an extension of linear time logic including past (LTL) with new operators that impose constraints on the accumulated weight along path fragments. The fragments are characterized by regular conditions formalized by deterministic finite automata (monitor DFA). This new logic covers properties expressible by several recently proposed formalisms. We study the model-checking problem for weighted transition systems, Markov chains and Markov decision processes with rational weights. While the general problem is undecidable, we provide algorithms and sharp complexity bounds for several sublogics that arise by restricting the monitoring DFA.
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线性时间逻辑的权重监测:复杂性和可判定性
许多重要的性能和可靠性度量可以形式化为权重函数的累加值。在本文中,我们引入了一个扩展的线性时间逻辑,包括过去(LTL)与新的算子施加约束的累积权沿路径片段。碎片的特征是由确定性有限自动机(监视器DFA)形式化的规则条件。这个新的逻辑涵盖了最近提出的几种形式表示的属性。研究了具有有理权的加权转移系统、马尔可夫链和马尔可夫决策过程的模型检验问题。虽然一般问题是不确定的,但我们为限制监视DFA产生的几个子逻辑提供了算法和明确的复杂性界限。
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