Resource bisimilarity and graded bisimilarity coincide

Resource bisimilarity has been proposed in the literature on concurrency theory as a notion of bisimilarity over labeled transition systems that takes into account the number of choices that a system has. Independently, g-bisimilarity has been defined over Kripke models as a suitable notion of bisimilarity for graded modal logic. This note shows that these two notions of bisimilarity coincide over image-finite Kripke frames.     

A ground-complete axiomatization of stateless bisimilarity over Linda

This paper offers a finite, ground-complete axiomatization of stateless bisimilarity over the tuple-space-based coordination language Linda. As stepping stones towards that result, axiomatizations of stateless bisimilarity over the sequential fragment of Linda without the nask primitive, and over the full sequential sub-language are given. It is also shown that stateless bisimilarity coincides with standard bisimilarity over the sequential fragment of Linda without the nask primitive.     

非确定型离散事件系统双模拟控制的实现

近年来,双模拟等价关系与离散事件系统监控理论相结合的研究引起了国内外许多学者的广泛关注.本文针对作者在前期工作中提出的非确定型离散事件系统的双模拟控制机制,进一步探讨其实现问题.利用投影映射对系统规范说明语言进行等价类划分,构造了一棵计算树,得到了一个判断规范说明是否具有基于模拟关系可观性的多项式算法,证明了双模拟控制机制是多项式时间算法可实现的.同时,通过对控制器配备具有存储和判断功能的模拟关系识别器,阐述了这种双模拟控制机制是物理可实现的.     

Deciding probabilistic bisimilarity over infinite-state probabilistic systems

We prove that probabilistic bisimilarity is decidable over probabilistic extensions of BPA and BPP processes. For normed subclasses of probabilistic BPA and BPP processes we obtain polynomial-time algorithms. Further, we show that probabilistic bisimilarity between probabilistic pushdown automata and finite-state systems is decidable in exponential time. If the number of control states in PDA is bounded by a fixed constant, then the algorithm needs only polynomial time. The work has been supported by the research centre Institute for Theoretical Computer Science (ITI), project No. 1M0545.     

A modal characterization of alternating approximate bisimilarity

Recently, alternating transition systems are adopted to describe control systems with disturbances and their finite abstract systems. In order to capture the equivalence relation between these systems, a notion of alternating approximate bisimilarity is introduced. This paper aims to establish a modal characterization for alternating approximate bisimilarity. Based on this result, we provide a link between specifications satisfied by the samples of control systems with disturbances and their finite abstractions. Moreover, a simple example is given to illustrate the application of such link in the design of controller of control systems.     

A Syntactical Approach to Weak (Bi-)Simulation for Coalgebras

In [19] Rutten introduced the notion of weak bisimulations and weak bisimilarity for coalgebras of the functor F(X) = X + O. In the present paper I will introduce a notion of weak bisimulation for coalgebras based on the syntax of their functors for a large class of functors. I will show that my definition does not only coincide with the definition from [19], but with the definition for labelled transition systems as well. The approach includes a definition of weak bisimulation for Kripke structures, which might be of interest in its own right.     

Branching bisimulation for probabilistic systems: Characteristics and decidability

We address the concept of abstraction in the setting of probabilistic reactive systems, and study its formal underpinnings for the strictly alternating model of Hansson. In particular, we define the notion of branching bisimilarity and study its properties by studying two other equivalence relations, viz. coloured trace equivalence and branching bisimilarity using maximal probabilities. We show that both alternatives coincide with branching bisimilarity. The alternative characterisations have their own merits and focus on different aspects of branching bisimilarity. Coloured trace equivalence can be understood without knowledge of probability theory and is independent of the notion of a scheduler. Branching bisimilarity, rephrased in terms of maximal probabilities gives rise to an algorithm of polynomial complexity for deciding the equivalence. Together they give a better understanding of branching bisimilarity. Furthermore, we show that the notions of branching bisimilarity in the alternating model of Hansson and in the non-alternating model of Segala differ: branching bisimilarity in the latter setting turns out to discriminate between systems that are intuitively branching bisimilar.     

Weak bisimilarity and regularity of context-free processes is EXPTIME-hard

We show that checking weak bisimulation equivalence of two context-free processes (also called BPA-processes) is EXPTIME-hard, even under the condition that the processes are normed. Furthermore, checking weak regularity (finiteness up to weak bisimilarity) for context-free processes is EXPTIME-hard as well. Adding a finite control of the minimal non-trivial size of 2 to the BPA process already makes weak bisimilarity undecidable.     

Weak bisimilarity between finite-state systems and BPA or normed BPP is decidable in polynomial time

We prove that weak bisimilarity is decidable in polynomial time between finite-state systems and several classes of infinite-state systems: context-free processes and normed basic parallel processes (normed BPP). To the best of our knowledge, these are the first polynomial algorithms for weak bisimilarity problems involving infinite-state systems.     

Causality versus true-concurrency

Category theory has been successfully employed to structure the confusing set-up of models and equivalences for concurrency: Winskel and Nielsen have related the standard models via adjunctions and (co)reflections while Joyal et al. have defined an abstract notion of equivalence, known as open map bisimilarity. One model has not been integrated into this framework: the causal trees of Darondeau and Degano. Here we fill this gap. In particular, we show that there is an adjunction from causal trees to event structures, which we bring to light via a mediating model, that of event trees. Further, we achieve an open map characterization of history preserving bisimilarity: the latter is captured by the natural instantiation of the abstract bisimilarity for causal trees.     

Deciding bisimilarity is<Emphasis Type="Italic">P</Emphasis>-complete

In finite labelled transition systems the problems of deciding strong bisimilarity, observation equivalence and observation congruence areP-complete under many—oneNC-reducibility. As a consequence, algorithms for automated analysis of finite state systems based on bisimulation seem to be inherently sequential in the following sense: the design of anNC algorithm to solve any of these problems will require an algorithmic breakthrough, which is exceedingly hard to achieve.     

A Behavioural Pseudometric based on λ–Bisimilarity

In order to describe approximate equivalence among processes, the notions of λ–bisimilarity and behavioural pseudometric have been introduced by Ying and van Breugel respectively. Van Breugel provides a distance function induced by λ–bisimilarity, and conjectures that his behavioural pseudometric coincides with this function. This paper is inspired by this conjecture. We give a negative answer for van Breugel's conjecture first. Moreover, we show that the distance function induced by λ–bisimilarity is a pseudometric on states, and provide a fixed point characterization of this pseudometric.     

Branching bisimulation congruence for probabilistic systems

A notion of branching bisimilarity for the alternating model of probabilistic systems, compatible with parallel composition, is defined. For a congruence result, an internal transition immediately followed by a non-trivial probability distribution is not considered inert. A weaker definition of branching bisimilarity for the same model has been given earlier. Here we show that our branching bisimulation is the coarsest congruence for parallel composition that is included in the weaker version. To support the use of the present equivalence as a reduction technique, we also show that probabilistic CTL formulae are preserved by our equivalence, and we provide a polynomial-time algorithm deciding branching bisimilarity.     

Causality Versus True-Concurrency

Category theory has been successfully employed to structure the confusing setup of models and equivalences for concurrency: Winskel and Nielsen have related the standard models via adjunctions and (co)reflections while Joyal et al. have defined an abstract notion of equivalence, known as open map bisimilarity. One model has not been integrated into this framework: the causal trees of Darondeau and Degano. Here we fill this gap. In particular, we show that there is an adjunction from causal trees to event structures, which we bring to light via a mediating model, that of event trees. Further, we achieve an open map characterization of history preserving bisimilarity: the latter is captured by the natural instantiation of the abstract bisimilarity for causal trees.     

From SOS Specifications to Structured Coalgebras: How to Make Bisimulation a Congruence

In this paper we address the issue of providing a structured coalgebra presentation of transition systems with algebraic structure on states determined by an equational specification Γ. More precisely, we aim at representing such systems as coalgebras for an endofunctor on the category of Γ-algebras. The systems we consider are specified by using a quite general format of SOS rules, the algebraic format, which in general does not guarantee that bisimilarity is a congruence.We first show that the structured coalgebra representation works only for systems where transitions out of complex states can be derived from transitions out of corresponding component states. This decomposition property of transitions indeed ensures that bisimilarity is a congruence. For a system not satisfying this requirement, next we propose a closure construction which adds context transitions, i.e., transitions that spontaneously embed a state into a bigger context or vice-versa. The notion of bisimulation for the enriched system coincides with the notion of dynamic bisimilarity for the original one, that is, with the coarsest bisimulation which is a congruence. This is sufficient to ensure that the structured coalgebra representation works for the systems obtained as result of the closure construction.     

(η,α)-互模拟的分层及判定算法

分层刻画是传统的互模拟概念研究中的一个重要内容,它为一些互模拟判定算法提供了理论基石。(η,α)-互模拟是一种带折扣的近似互模拟概念,其定义蕴涵着一种折扣思想:在比较系统差异时,越晚出现的差异越不重要。为(η,α)-互模拟建立分层刻画,将清晰地揭示这种折扣思想。此外,由于(η,α)-互模拟一般不是等价关系,所以传统的互模拟判定算法中常用的最粗划分方法不适用于(η,α)-互模拟的判定,基于(η,α)-互模拟的分层刻画给出一种该互模拟的判定算法。还提供一个简单的例子用于说明(η,α)-互模拟及其判定算法在描述实现与规范之间关系时的应用。     

Decidability of Branching Bisimulation on Normed Commutative Context-Free Processes

We investigate normed commutative context-free processes (Basic Parallel Processes). We show that branching bisimilarity admits the bounded response property: in the Bisimulation Game, Duplicator always has a response leading to a process of size linearly bounded with respect to the Spoiler’s process. The linear bound is effective, which leads to decidability of branching bisimilarity. For weak bisimilarity, we are able merely to show existence of some linear bound, which is not sufficient for decidability. We conjecture however that the same effective bound holds for weak bisimilarity as well. We suppose that further elaboration of novel techniques developed in this paper may be sufficient to demonstrate decidability.     

Equivalences for Silent Transitions in Probabilistic Systems: (Extended Abstract)

We address abstraction in the setting of probabilistic reactive systems, and study its formal underpinnings for the strictly alternating model. In particular, we define the notion of branching bisimilarity and study its properties by studying two other equivalence relations, viz. coloured trace equivalence and branching bisimilarity using maximal probabilities. We show that both alternatives coincide with branching bisimilarity. The alternative characterisations have their own merits and focus on different aspects of branching bisimilarity. Together they give a better understanding of branching bisimilarity. A crucial observation, and, in fact a major motivation for this work is that the notions of branching bisimilarity in the alternating and in the non-alternating model differ, and that the latter one discriminates between systems that are intuitively branching bisimilar.     

Unprovability of the logical characterization of bisimulation

We quickly review labelled Markov processes (LMP) and provide a counterexample showing that in general measurable spaces, event bisimilarity and state bisimilarity differ in LMP. This shows that the Hennessy-Milner logic proposed by Desharnais does not characterize state bisimulation in non-analytic measurable spaces. Furthermore we show that, under current foundations of Mathematics, such logical characterization is unprovable for spaces that are projections of a coanalytic set. Underlying this construction there is a proof that stationary Markov processes over general measurable spaces do not have semi-pullbacks.     

泛化双向相似连接

相似连接是数据管理领域的一个热门话题,已在社会生产生活中得到广泛应用.然而,现有的相似连接方法并不能满足真实世界不断增长的客观需求.本文通过引入定义在多种数据类型上的“满足”操作符和每条数据的独立阈值定义了一种新的相似连接——泛化双向相似连接.这种连接扩展了相似连接的应用范围.同时,本文还提出了两种高效的解决泛化双向相似连接问题的方法：子连接集算法和映射-过滤-验证算法.在真实和合成数据集上的大量实验结果展示了所提方法的正确性和有效性.