STGA的变种及其互模拟验证

为刻画和验证无穷值域上的传值进程,Ｈｅｎｎｅｓｓｙ和Ｌｉｎ先后提出符号迁移图（ＳＴＧ）和带赋值符号迁移图（ＳＴＧＡ）作为传值进程的语义表示模型,并给出了相应的强互模拟算法．为将该方法推广至实际应用中更常用的弱互模拟等价和观察同余的验证问题,该文首先引入了ＳＴＧＡ的一个变种,它与原模型的不同之处在于将符号迁移上赋值和符号动作的执行次序颠倒,因而可定义些种ＳＴＧＡ结果间的符号双迁移关系．文中提出了从正     

嵌套谓词等式系与弱互模拟

带赋值符号迁移图是一般传值进程的语义模型,其强互模拟等价可以归结为谓词等式系的最大解.该文将这一结果推广到弱互模拟等价,为此,引入嵌套谓词等式系的概念,并提出算法,将带赋值符号迁移图的弱互模拟等价归结为形如E₂μE₁的嵌套谓词等式系的最大解.     

时间符号迁移图及其互模拟判定

引入时间符号迁移图的概念，作为既涉及通讯又具有实时性的并发系统的模型，该文给出了这种迁移图时间互模拟的算法，并证明了该算法的正确性。     

数据传送进程的符号互模拟*

本文提出数据传送进程的符号迁移语义，引入符号互模拟的概念，证明了两个进程在传统意义下互模拟当且仅当它们符号互模拟．由于无穷域上的数据传送进程的传统迁移图是无穷的，而其中相当一部分的符号迁移图是有穷的，文章的结果为在有穷时间和空间内判定这类进程的互模拟关系开辟了可能性．     

数据传送进程的符号互模拟

本提出数据传送进程的符号迁移语义，引入符号互模拟的概念，证明了两个进程在传统意义下互模拟当且仅当它们符号互模拟。我穷域上的数据传送进程的传统迁移图是无穷的而其中相当的一部分的符号迁移图是有穷的，章的结果为在有穷时间和空间内判定这类进程的互模拟关系开辟了可能性。     

传值系统的互模拟与谓词等式系

本文引入描述传值并系统的新模型“带赋值符号迁移图（ＳＴＧＡ）”推广了Ｈｅｎｎｅｓｓｙ和Ｌｉｎ提出的“符号迁移图”的概念，允许迁移上带有赋值，从而能将更大的一类传值系统表示为有穷状态图，ＳＴＧＡ的中车优点是在并行运算不封闭，文中给给ＳＴＧＡ的操作语义，在此基础上定义了ＳＴＧＡ的互模拟等价关系，为了刻划ＳＴＧＡ的互模拟，以谓词等式系的形式在一阶逻辑的正子集中扩充了最大和最小不动点，并设计了一个算法将Ｓ     

类型化π演算的双代数语义

证明互模拟同余通常冗长且易出错.双代数为解决该问题提供统一的框架:若行为函子保持弱回拉,共代数范畴到基范畴的忘却函子有右伴函子,则最大共代数互模拟同余.但已有双代数理论建模类型化π演算存在以下困难:行为函子不保持弱回拉,进程互模拟与共代数互模拟不一致.为解决以上两个问题,用稠密拓扑导出布尔范畴作为语义范畴,令行为函子保持弱回拉;定义一类行为函子,使最大进程互模拟与最大共代数互模拟一致,而迟语义和早语义对应的行为函子属于该类函子.进而给出π演算最大进程互模拟同余的双代数模型,为进一步应用双代数框架对其他复杂演算建模奠定了理论基础.     

连续时间Markov决策过程互模拟等价及逻辑保持

模型检测中,Markov决策过程可以建模具有不确定性的系统,然而状态空间爆炸问题将会影响系统验证的成败与效率,互模拟等价可以用于系统状态的简约.在强互模拟关系的基础上,给出Markov决策过程模型弱互模拟等价关系的概念,导出了连续时间Markov决策过程及其内嵌离散时间Markov决策过程互模拟等价关系的内在联系;在强互模拟等价关系逻辑特征保持的基础上,给出弱互模拟等价关系下的逻辑保持性质,证明了弱互模拟等价的两个状态,同时满足除下一步算子外的连续随机逻辑公式,从而可以将原模型中的验证问题转换为简约后模型的验证问题,提高验证的效率.     

非对称χ≠-演算的基同余

该文研究非对称χ^≠-演算的基同余．文中引入一组L-互模拟关系,并确定基互模拟就是由L-互模拟定义导出的12个互异的互模拟关系中的最小关系,给出了某些L-互模拟的开模拟性质,利用开模拟性质引入开基互模拟概念,并证明开基互模拟与基互模拟是一致的,构造了基于基同余的可靠和完备的等式系统,最后给出了基同余的完备性定理．     

混合语义时间Petri网的特征条件及时间性质

针对时间Petri网现有强、弱语义模型在调度分析上存在的缺陷以及凝练调度一致性问题和调度时限性问题,提出混合语义模型解决方案,并给出混合语义模型的特征条件,比较混合语义模型与强、弱语义模型的时间互模拟能力,证明混合语义模型的正确性和时间行为的不可替代性。     

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.     

Computing maximal weak and other bisimulations

We present and compare several algorithms for computing the maximal strong bisimulation, the maximal divergence-respecting delay bisimulation, and the maximal divergence-respecting weak bisimulation of a generalised labelled transition system. These bisimulation relations preserve CSP semantics, as well as the operational semantics of programs in other languages with operational semantics described by such GLTSs and relying only on observational equivalence. They can therefore be used to combat the space explosion problem faced in explicit model checking for such languages. We concentrate on algorithms which work efficiently when implemented rather than on ones which have low asymptotic growth.     

Bisimulations for a calculus of broadcasting systems

We develop a theory of bisimulation equivalence for the broadcast calculus CBS. Both the strong and weak versions of bisimulation congruence we study are justified in terms of a characterisation as the largest CBS congruences contained in an appropriate version of barbed bisimulation. We then present sound and complete proof systems for both the strong and weak congruences over finite terms. The first system we give contains an infinitary proof rule to accommodate input prefixes. We improve on this by presenting a unitary proof system where judgements are relative to properties of the data domain.     

Notes on Generative Probabilistic Bisimulation

In this notes we consider the model of Generative Probabilistic Transition Systems, and Baier and Hermanns' notion of weak bisimulation defined over them. We prove that, if we consider any process algebra giving rise to a Probabilistic Transition System satisfying the condition of regularity and offering prefixing, interleaving, and guarded recursion, then the coarsest congruence that is contained in weak bisimulation is strong bisimulation.     

Computing strong and weak bisimulations for psi-calculi

We present a symbolic transition system and strong and weak bisimulation equivalences for psi-calculi, and show that they are fully abstract with respect to bisimulation congruences in the non-symbolic semantics. A procedure which computes the most general constraint under which two agents are bisimilar is developed and proved correct.A psi-calculus is an extension of the pi-calculus with nominal data types for data structures and for logical assertions representing facts about data. These can be transmitted between processes and their names can be statically scoped using the standard pi-calculus mechanism to allow for scope migrations. Psi-calculi can be more general than other proposed extensions of the pi-calculus such as the applied pi-calculus, the spi-calculus, the fusion calculus, or the concurrent constraint pi-calculus.Symbolic semantics are necessary for an efficient implementation of the calculus in automated tools exploring state spaces, and the full abstraction property means the symbolic semantics makes exactly the same distinctions as the original.     

Decision procedures and graph reductions for bisimulation equivalences part 1

In Process Algebra, processes are often specified in a framework of bisimulation semantics. The notion of bisimulation therefore plays an important role.

In this paper some existing and new decision methods are presented for strong bisimulation, τ-bisimulation and η-bisimulation. Each of these bisimulation equivalences corresponds to a certain abstraction mechanism.

In strong bisimulation, all events in a system are treated equally whereas τ-bisimulation takes into account the silent step τ; η-bisimulation was introduced recently for an alternative silent step η that is less abstract than τ. It is shown that the problem of η-bisimulation decision can be reduced to an abstract graph partitioning problem called the Product Relational Coarsest Partition problem. Special attention is paid to computational complexity of the decision methods.

As it turns out. finite process graphs can be reduced to unique minimal normalforms under all three bisimulation semantics mentioned.

The last section demonstrates how the decision methods can be used with a particular algebraic model to enable effective verification of specifications.     

Modal Logics for Observation Equivalences

In our paper [RM02a] we describe an approach to weak bisimulation for coalgebras and show that parts of the theory of universal coalgebra (with strong bisimulation) can be obtained when considering coalgebras with weak bisimulations and weak homomorphisms. In the present paper we focus on uniformly adapting modal logics that characterise strong bisimulation for coalgebras to several kinds of observation equivalences.     

Multi-core symbolic bisimulation minimisation

We introduce parallel symbolic algorithms for bisimulation minimisation, to combat the combinatorial state space explosion along three different paths. Bisimulation minimisation reduces a transition system to the smallest system with equivalent behaviour. We consider strong and branching bisimilarity for interactive Markov chains, which combine labelled transition systems and continuous-time Markov chains. Large state spaces can be represented concisely by symbolic techniques, based on binary decision diagrams. We present specialised BDD operations to compute the maximal bisimulation using signature-based partition refinement. We also study the symbolic representation of the quotient system and suggest an encoding based on representative states, rather than block numbers. Our implementation extends the parallel, shared memory, BDD library Sylvan, to obtain a significant speedup on multi-core machines. We propose the usage of partial signatures and of disjunctively partitioned transition relations, to increase the parallelisation opportunities. Also our new parallel data structure for block assignments increases scalability. We provide SigrefMC, a versatile tool that can be customised for bisimulation minimisation in various contexts. In particular, it supports models generated by the high-performance model checker LTSmin, providing access to specifications in multiple formalisms, including process algebra. The extensive experimental evaluation is based on various benchmarks from the literature. We demonstrate a speedup up to 95\(\times \) for computing the maximal bisimulation on one processor. In addition, we find parallel speedups on a 48-core machine of another 17\(\times \) for partition refinement and 24\(\times \) for quotient computation. Our new encoding of the reduced state space leads to smaller BDD representations, with up to a 5162-fold reduction.

     

Towards a theory of bisimulation for the higher-order process calculi

In this paper, a labelled transition semantics for higher-order process calculi is studied. The labelled transition semantics is relatively clean and simple, and corresponding bisimulation equivalence can be easily formulated based on it. And the congruence properties of the bisimulation equivalence can be proved easily. To show the correspondence between the proposed semantics and the well-established ones, the bisimulation is characterized as a version of barbed equivalence and a version of context bisimulation.