基于广义可能性测度的模型检测

给出了基于广义可能性测度的计算树逻辑的扩张(Generalized Possibilistic Computation Tree Logic's expansion,GPoCTL*)、计算树逻辑的约简(Generalized Possibilistic Computation Tree Logic's reduction,GPoCTL?)以及带回报的计算树逻辑(Generalized Possibilistic Reward Computation Tree Logic,GPoRCTL)的语构和语义.     

具有DP的广义可能性模糊时态CTL模型检测

为了增强计算树逻辑在时序上的表达能力,以广义可能性测度、决策过程和计算树逻辑为基础,研究了具有决策过程的广义可能性模糊时态计算树逻辑的模型检测。首先采用广义可能性决策过程作为系统模型;然后引入模糊时态算子,构造了模糊时态计算树逻辑并给出其在广义可能性测度下的语义,得到新的广义可能性模糊时态计算树逻辑用来描述系统属性;最后在广义可能性调度下通过模糊矩阵运算讨论了"soon、within、last、nearly"等几类模糊时态连接词的具体计算方法,给出相应的模型检测算法。经验证明,广义可能性模糊时态计算树逻辑是广义可能性计算树逻辑在模糊时序上的扩充,具有更强的表达能力。     

基于可能性测度的计算树逻辑CTL*与可能性互模拟

提出了基于可能性测度的计算树逻辑CTL*(PoCTL*)的概念。给出了在可能的Kripke结构中可能性互模拟的定义并对其性质进行了详细的探讨。对商可能性Kripke结构及其相关构造进行了特别的研究。     

广义可能性计算树逻辑的两种范式

计算树逻辑(computation tree logic,CTL)的范式在模型检测方法中具有重要意义,但基于广义可能性测度的计算树逻辑的范式尚未有系统研究。为了进一步完善广义可能性计算树(generalized possibilistic computation tree logic,GPo CTL)理论,在现有的广义可能性计算树逻辑理论的基础上,参考经典计算树逻辑的范式,给出了广义可能性计算树逻辑的两种不同的范式——正态范式(positive normal form,PNF)和存在范式(existential normal form,ENF),及其对应的语构和语义解释。最后利用归纳假设法证明了任意的广义可能性计算树逻辑公式都有与之等价的PNF公式和ENF公式。     

广义可能性决策过程的计算树逻辑模型检测

模型检测作为一种形式化验证技术,已被广泛应用于各种并发系统的正确性验证。针对具有非确定性选择和广义可能性分布的并发系统,引入广义可能性决策过程作为此类系统的模型;给出描述其性质的规范语言广义可能性计算树逻辑的概念;研究此类系统的广义可能性计算树逻辑模型检测问题。结论表明,其模型检测算法的时间复杂度也为多项式时间。所获得的结果扩大了广义可能性测度在模型检测中的应用范围。     

基于可能性测度的计算树逻辑

首先,提出了可能的Kripke结构的定义,建立了可能的Kripke结构的可能性测度空间,并分析了可能的Kripke结构的一系列性质,即任一路径转移的可能性可由其初始状态的可能性分布与各转移的可能性取下确界而得到;依据可能的Kripke结构所定义的可能性测度具有其合理性等等。其次,给出了可能性计算树逻辑(PoCTL)的概念,讨论了两个PoCTL状态公式以及PoCTL与经典计算树逻辑(CTL)公式的等价性。最后,证明了PoCTL公式有与CTL*公式中"一致性"相对应的公式。     

广义可能性计算树逻辑和计算树逻辑的关系

广义可能性计算树逻辑(generalized possibilistic computation tree logic,GPo CTL)在不确定性模型检测中扮演着非常重要的角色,但其表达能力还尚未研究全面。为此,讨论了GPo CTL与计算树逻辑(computation tree logic,CTL)表达能力之间的关系。首先定义了区间广义可能性计算树逻辑(interval generalized pos-sibilistic computation tree logic,IGPo CTL),并给出了IGPo CTL公式和CTL公式等价的定义。然后证明了CTL是IGPo CTL的一个真子类,因为IGPo CTL是GPo CTL的一种简单分明化形式,则CTL可看作GPo CTL的一个真子类。此外,还给出了IGPo CTL公式和CTL公式α-等价的定义,并得出了一些更一般的结果。     

具有多值决策过程的广义可能性计算树逻辑模型检测

模型检测是一种自动验证软硬件系统行为的有效技术。为了对包含非确定性信息、不一致信息的并发系统进行形式化验证,在可能性理论、多值逻辑的基础上,研究了具有多值决策过程的广义可能性多值计算树逻辑模型检测算法,及其在检验非确定性系统中的具体应用。首先构造了多值决策过程作为系统模型,用多值计算树逻辑描述系统属性。然后给出具有多值决策过程的广义可能性多值计算树逻辑的模型检测算法,该算法将模型检测的具体问题转换为多项式时间内的模糊矩阵运算。最后就包含非确定性选择的多值系统的模型检测问题,给出一个具体的应用实例。     

基于可能性理论的导弹攻防作战系统态势分析

在导弹武器系统攻防作战中,提出一种基于可能性理论的态势分析模型。由模糊Petri网的复合与规则分别计算敌我双方导弹体系的可能性测度作战效能、必然性测度作战效能以及可信性测度作战效能,通过比较双方的相应测度值,得出战场态势等级,从而辅助作战人员进行决策。实例表明,该模型有效且可行。     

可能性理论与不相容知识处理

Ｄ．Ｄｕｂｏｉｓ和Ｈ．Ｐｒａｄｅ提出的可能性逻辑是一种基于可能性理论的非经典逻辑，主要和于不确定证据推理。可能性逻辑不同于模糊逻辑，因为模糊逻辑处理非布尔公式，其命题中包模糊谓词，而可能性逻辑处理布尔公式，其中只包含经典命题的和谓词。本文尝试在可能性理论的框架下进行不相容知识库的维护和问题求解。这里的知识表示是基于可能性逻辑的。为此，我们提出了两种不同的方法：第一种方法在计算命题可信度时，要考虑所     

On cool congruence formats for weak bisimulations

In TCS 146, Bard Bloom presented rule formats for four main notions of bisimulation with silent moves. He proved that weak bisimulation equivalence is a congruence for any process algebra defined by WB cool rules, and established similar results for rooted weak bisimulation (Milner’s “observational congruence”), branching bisimulation and rooted branching bisimulation. This study reformulates Bloom’s results in a more accessible form and contributes analogues for (rooted) η-bisimulation and (rooted) delay bisimulation. Moreover, finite equational axiomatisations of rooted weak bisimulation equivalence are provided that are sound and complete for finite processes in any RWB cool process algebra. These require the introduction of auxiliary operators with lookahead, and an extension of Bloom’s formats for this type of operator with lookahead. Finally, a challenge is presented for which Bloom’s formats fall short and further improvement is called for.     

A Branching Time Temporal Framework for Quantitative Reasoning

Temporal logics such as Computation Tree Logic (CTL) and Linear Temporal Logic (LTL) have become popular for specifying temporal properties over a wide variety of planning and verification problems. In this paper we work towards building a generalized framework for automated reasoning based on temporal logics. We present a powerful extension of CTL with first-order quantification over the set of reachable states for reasoning about extremal properties of weighted labeled transition systems in general. The proposed logic, which we call Weighted Quantified Computation Tree Logic (WQCTL), captures the essential elements common to the domain of planning and verification problems and can thereby be used as an effective specification language in both domains. We show that in spite of the rich, expressive power of the logic, we are able to evaluate WQCTL formulas in time polynomial in the size of the state space times the length of the formula. Wepresent experimental results on the WQCTL verifier.     

NCES-based modelling and CTL-based verification of reconfigurable embedded control systems

This paper (This work is done in the research laboratory of Prof. Dr. Hans-Michael Hanisch at the Martin Luther University in Germany, and it is supported by the Alexander von Humboldt foundation in Germany under the reference TUN1127196STP.) deals with automatic reconfigurations of safe embedded control systems following the component-based International Industrial Standard IEC61499 in which a Function Block (FB) is an event triggered software component owning data and a control application is a network of blocks. We define a new semantics of reconfigurations that allow automatic improvements of system performances at run-time even if there are no hardware faults. We apply this new semantics on two Benchmark Production Systems developed in our research laboratory according to this industrial technology. We classify thereafter into three forms all possible reconfiguration scenarios to be applied at run-time by a well-defined agent in order to adapt the system to its environment according to well-defined conditions. The agent is modelled by nested state machines according to the formalism Net Condition/Event Systems (NCES) which is an extension of Petri nets. In order to satisfy user requirements, we specify functional and non-functional properties according to the well-known temporal logic “Computation Tree Logic” (CTL) as well as its extensions eCTL and TCTL, and we apply the model checker SESA to check the whole agent-based architecture of the reconfigurable system.     

On the computational complexity of bisimulation, redux

Paris Kanellakis and the second author (Smolka) were among the first to investigate the computational complexity of bisimulation, and the first and third authors (Moller and Srba) have long-established track records in the field. Smolka and Moller have also written a brief survey about the computational complexity of bisimulation [ACM Comput. Surv. 27(2) (1995) 287]. The authors believe that the special issue of Information and Computation devoted to PCK50: Principles of Computing and Knowledge: Paris C. Kanellakis Memorial Workshop represents an ideal opportunity for an up-to-date look at the subject.     

计算实对称矩阵广义特征值问题的并行算法

矩阵广义特征值问题是科学计算与工程应用中的一个重要的研究课题。文章探讨了近年来计算对称矩阵广义特征值问题的并行算法,并着重介绍了二分法、分治算法、同伦连续法和迭代算法。     

Fuzzy measures and generalized Möbius transform

Generalized Möbius transform is recalled and applied in some special cases. The relationship with the standard Möbius transform is shown. By means of the generalized Möbius transform, a general concept of k -order additivity independent of the cardinality of the underlying space is introduced. The relationship of the Choquet integral and the Lebesgue integral by means of the generalized Möbius transform is clarified. Also possibilistic Möbius transform and k -order possibility measures are introduced. Finally, some examples are given, including the characterization of de Finetti's discrete lower probabilities.     

Abstraction and approximation in fuzzy temporal logics and models

Recently, by defining suitable fuzzy temporal logics, temporal properties of dynamic systems are specified during model checking process, yet a few numbers of fuzzy temporal logics along with capable corresponding models are developed and used in system design phase, moreover in case of having a suitable model, it suffers from the lack of a capable model checking approach. Having to deal with uncertainty in model checking paradigm, this paper introduces a fuzzy Kripke model (FzKripke) and then provides a verification approach using a novel logic called Fuzzy Computation Tree Logic* (FzCTL*). Not only state space explosion is handled using well-known concepts like abstraction and bisimulation, but an approximation method is also devised as a novel technique to deal with this problem. Fuzzy program graph, a generalization of program graph and FzKripke, is also introduced in this paper in consideration of higher level abstraction in model construction. Eventually modeling, and verification of a multi-valued flip-flop is studied in order to demonstrate capabilities of the proposed models.     

Testing equivalence as a bisimulation equivalence

In this paper we show how the testing equivalences and preorders on transition systems may be interpreted as instances of generalized bisimulation equivalences and prebisimulation preorders. The characterization relies on defining transformations on the transition systems in such a way that the testing relations on the original systems correspond to (pre)bisimulation relations on the altered systems. On the basis of these results, it is possible to use algorithms for determining the (pre)bisimulation relations in the case of finite-state transition systems to compute the testing relations.     

Decision-making based on approximate and smoothed Pareto curves

We consider bicriteria optimization problems and investigate the relationship between two standard approaches to solving them: (i) computing the Pareto curve and (ii) the so-called decision maker’s approach in which both criteria are combined into a single (usually nonlinear) objective function. Previous work by Papadimitriou and Yannakakis showed how to efficiently approximate the Pareto curve for problems like Shortest Path, Spanning Tree, and Perfect Matching. We wish to determine for which classes of combined objective functions the approximate Pareto curve also yields an approximate solution to the decision maker’s problem. We show that an FPTAS for the Pareto curve also gives an FPTAS for the decision-maker’s problem if the combined objective function is growth bounded like a quasi-polynomial function. If the objective function, however, shows exponential growth then the decision-maker’s problem is NP-hard to approximate within any polynomial factor. In order to bypass these limitations of approximate decision making, we turn our attention to Pareto curves in the probabilistic framework of smoothed analysis. We show that in a smoothed model, we can efficiently generate the (complete and exact) Pareto curve with a small failure probability if there exists an algorithm for generating the Pareto curve whose worst-case running time is pseudopolynomial. This way, we can solve the decision-maker’s problem w.r.t. any non-decreasing objective function for randomly perturbed instances of, e.g. Shortest Path, Spanning Tree, and Perfect Matching.     

Deciding orthogonal bisimulation

Bergstra, Ponse and van der Zwaag introduced in 2003 the notion of orthogonal bisimulation equivalence on labeled transition systems. This equivalence is a refinement of branching bisimulation, in which consecutive tau’s (silent steps) can be compressed into one (but not zero) tau’s. The main advantage of orthogonal bisimulation is that it combines well with priorities. Here we solve the problem of deciding orthogonal bisimulation equivalence in finite (regular) labeled transition systems. Unlike as in branching bisimulation, in orthogonal bisimulation, cycles of silent steps cannot be eliminated. Hence, the algorithm of Groote and Vaandrager (1990) cannot be adapted easily. However, we show that it is still possible to decide orthogonal bisimulation with the same complexity as that of Groote and Vaandrager’s algorithm. Thus if n is the number of states, and m the number of transitions then it takes O(n(m + n)) time to decide orthogonal bisimilarity on finite labeled transition systems, using O(m + n) space. J. Parrow