From the perspective of attribute decomposition, there are a variety of software trustworthiness metric models. However, little attention has been paid to using more rigorous methods and to performing theoretical validation. Axiomatic methods formalise the empirical understanding of software attributes through defining ideal metric properties. They can offer precise terms for the software attributes' quantification. We have utilised them to assess software trustworthiness on the basis of attribute decomposition, presented four properties, constructed a software trustworthiness measure (STMBDA for short). In this paper, we extend the set of properties, introduce two new properties, namely non-negativity and proportionality, and perfect substitutability and expectability. We verify the theoretical rationality of STMBDA by demonstrating that it conforms to the new property set and the empirical validity by evaluating the trustworthiness of 23 spacecraft software. The validation results show that STMBDA is able to effectively assess the spacecraft software trustworthiness and identify weaknesses in the development process.

Modal logics and behavioral equivalences play an important role in the specification and verification of concurrent systems. In this paper, we first present a new notion of bisimulation for nondeterministic fuzzy transition systems, which is distribution based and coarser than state-based bisimulation appeared in the literature. Then, we define a distribution-based bisimilarity metric as the least fixed point of a suitable monotonic function on a complete lattice, which is a behavioral distance and is a more robust way of formalizing behavioral similarity between states than bisimulations. We also propose an on-the-fly algorithm for computing the bisimilarity metric. Moreover, we present a fuzzy modal logic and provide a sound and complete characterization of the bisimilarity metric. Interestingly, this characterization holds for a class of fuzzy modal logics. In addition, we show the nonexpansiveness of a typical parallel composition operator with respect to the bisimilarity metric, which makes compositional verification possible.

The behavioural distance is a more robust way of formalising behavioural similarity between states than bisimulations. The smaller the distance, the more alike the states are. It is helpful for quantitative verifications of concurrent systems. The main contribution of this paper is an effective procedure for computing behavioural distance introduced by Cao et al. (IEEE Transactions on Fuzzy Systems, 21 (2013) 735-747). The time complexity of the algorithm is O(n5m3lg n), where n is the number of states and m is the number of transitions in the underlying transition systems. The key step in this algorithm is to compute the distance between two distributions, which is defined as the value of a mathematical programming problem (MP). In this process, some interesting properties about solutions of a fuzzy system, which is a constraint of the MP, are discussed.

To model and analyze systems with multi-valued information, in this paper, we present an extension of Kripke structures in the framework of complete residuted lattices, which we will refer to as lattice-valued Kripke structures (LKSs). We then show how the traditional trace containment and equivalence relations, can be lifted to the lattice-valued setting, and we introduce two families of lattice-valued versions of the relations. Further, we explore some interesting properties of these relations. Finally, we provide logical characterizations of our relations by a natural extension of linear temporal logic.

In order to describe the requirement of spatial and temporal consistency of cyber-physical systems, a specification language called as STeC was proposed by Chen in [1]. In this paper, we focus on the theory of semantics of STeC. After simply restating the syntax and operational semantics, we mainly establish the denotational semantics of STeC. To investigate the reasonability of the denotational semantics, an abstract theorem is given to show the soundness and completeness of the denotational semantics. Finally, a simple case about China Gaotie (which means High-speed train) is given to show how to compute the operational and denotational semantics.

Many researchers suggested extending bisimilarity to quantitative versions to avoid the rigidity of classical bisimilarity. To explore the relation between different notions of approximate bisimilarity mentioned in literature, in this paper, we present a quantitative extension of doubly labeled transition systems, MDLTS, where its states and actions form metric spaces. We then introduce two notions of approximate bisimilarity, (η, λ)-bisimilarity and (η, λ, α)-bisimilarity, and discuss their basic property. We also consider the special kind of (η, λ)-bisimilarity, λ-bisimilarity to characterize the branching distance with arbitrary discount α of metric labeled transition system. Finally, we discuss the translation between metric transition system and MDLTS which preserves the approximate bisimilarity.