Most fairness assumptions used for verifying liveness properties are criticised for being too strong or unrealistic. On the other hand, justness, arguably the minimal fairness assumption required for the verification of liveness properties, is not preserved by classical semantic equivalences, such as strong bisimilarity. To overcome this deficiency, we introduce a finer alternative to strong bisimilarity, called enabling preserving bisimilarity. We prove that this equivalence is justness-preserving and a congruence for all standard operators, including parallel composition.
Establishing equivalences between programs or systems is crucial both for verifying correctness of programs, by establishing that two implementations are equivalent, and for justifying optimisations and program transformations, by establishing that a modified program is equivalent to the source one. There exist several equivalence relations for programs, and bisimulations are among the most versatile of these equivalences. Among bisimulation relations one distinguishes strong bisimulation, that requires that each action of a program is simulated by a single action of the equivalent program, a …
A New Branching Bisimulation for Probabilistic Processes
College of Computer and Information Science, Southwest University（西南大学计算机与信息科学学院）；Hunan University of Arts and Science（湖南文理学院）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；School of Mathematics and Statistics, Hubei Minzu University（湖北民族大学数学与统计学院）
We introduce polynomial couplings, a generalization of probabilistic couplings, to develop an algorithm for the computation of equivalence relations which can be interpreted as a lifting of probabilistic bisimulation to polynomial differential equations, a ubiquitous model of dynamical systems across science and engineering. The algorithm enjoys polynomial time complexity and complements classical partition-refinement approaches because: (a) it implements a local exploration of the system, possibly yielding equivalences that do not necessarily involve the inspection of the whole system of diff…
Bisimulations and Modal Logics for Higher Dimensional Automata
Norwegian University of Science and Technology（挪威科技大学）；University of Edinburgh（爱丁堡大学）；University of New South Wales（新南威尔士大学）；University of Warsaw（华沙大学）
We present a bisimulation relation for neighbourhood spaces, a generalisation of topological spaces. We show that this notion, path preserving bisimulation, preserves formulas of the spatial logic SLCS. We then use this preservation result to show that SLCS cannot express standard topological properties such as separation and connectedness. Furthermore, we compare the bisimulation relation with standard modal bisimulation and modal bisimulation with converse on graphs and prove it coincides with the latter.
We define a new logic-induced notion of bisimulation (called $ρ$-bisimulation) for coalgebraic modal logics given by a logical connection, and investigate its properties. We show that it is structural in the sense that it is defined only in terms of the coalgebra structure and the one-step modal semantics and, moreover, can be characterised by a form of relation lifting. Furthermore we compare $ρ$-bisimulations to several well-known equivalence notions, and we prove that the collection of bisimulations between two models often forms a complete lattice. The main technical result is a Hennessy-M…
A Companion of "Relating Strong Behavioral Equivalences for Processes with Nondeterminism and Probabilities"
在TCS上发表的论文“Relating Strong Behavioral Equivalences for Processes with Nondeterminism and Probabilities”中，我们对非确定性和概率过程的行为等价进行了比较。特别是，我们考虑强跟踪，故障，测试和互模拟等价。对于每一组这些等价物，我们研究了三种不同的方法，不同的事件的概率进行比较的方式时，通过确定性的选择解决三种变体的鉴别力。已建立的关系总结在所谓的频谱中。然而，我们在那篇论文中考虑的等价性只是Rob van Glabbeek介绍的非确定性系统的等价性的原始谱中所考虑的等价性的一小部分。在这篇姊妹论文中，我们通过考虑迹等价的变体（完成迹等价）、附加装饰迹等价（故障迹、就绪迹和就绪迹等价）和互模拟等价的变体（模拟、完成模拟、故障模拟和就绪模拟前序的内核）来扩大谱。此外，我们研究了如何频谱变化时，使用随机化的，而不是确定性的。
In this paper we investigate the equational theory of (the restriction, relabelling, and recursion free fragment of) CCS modulo rooted branching bisimilarity, which is a classic, bisimulation-based notion of equivalence that abstracts from internal computational steps in process behaviour. Firstly, we show that CCS is not finitely based modulo the considered congruence. As a key step of independent interest in the proof of that negative result, we prove that each CCS process has a unique parallel decomposition into indecomposable processes modulo branching bisimilarity. As a second main contri…
We present an extension of System F with higher-order context-free session types. The mixture of functional types with session types has proven to be a challenge for type equivalence formalization: whereas functional type equivalence is often rule-based, session type equivalence usually follows a semantic approach based on bisimulations. We propose a unifying approach that handles the equivalence of functional and session types together. We present three notions of type equivalence: a syntactic rule-based version, a semantic bisimulation-based version, and an algorithmic version by reduction t…
Description logics (DLs) are a suitable formalism for representing knowledge about domains in which objects are described not only by attributes but also by binary relations between objects. Fuzzy extensions of DLs can be used for such domains when data and knowledge about them are vague and imprecise. One of the possible ways to specify classes of objects in such domains is to use concepts in fuzzy DLs. As DLs are variants of modal logics, indiscernibility in DLs is characterized by bisimilarity. The bisimilarity relation of an interpretation is the largest auto-bisimulation of that interpret…
Timed automata (TA) are a well-established formalism for specifying discrete-state/continuous-time behavior of time-critical reactive systems. Concerning the fundamental analysis problem of comparing a candidate implementation against a specification, both given as TA, it has been shown that timed trace equivalence is undecidable, whereas timed bisimulation equivalence is decidable. The corresponding proof utilizes region graphs, a finite, but generally very space-consuming characterization of TA semantics. Hence, most practical TA tools utilize zone graphs instead, a symbolic and generally mo…
This paper shows how we can make use of an asynchronous transition system, whose transitions are labelled with events and which is equipped with a notion of independence of events, to define non-interleaving semantics for the applied $π$-calculus. The most important notions we define are: Start-Termination or ST-bisimilarity, preserving duration of events; and History-Preserving or HP- bisimilarity, preserving causality. We point out that corresponding similarity preorders expose clearly distinctions between these semantics. We draw particular attention to the distinguishing power of HP failur…
Univ.\ Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France；Inria, Univ.\ Lille, CNRS, Centrale Lille, UMR 9189 CRIStAL, F-59000 Lille, France
Step net bisimulation is a coinductive behavioral relation for finite Petri nets, which is a smooth generalization of the definition of standard step bisimulation \cite{NT84} on finite Petri nets. Its induced equivalence offers an alternative, much simpler characterization of causal-net bisimilarity \cite{G15,Gor22}, as it does not resort to any causality structure, and of structure-preserving bisimilarity \cite{G15}, as it does not require bijective mappings between related markings. We show that step net bisimilarity can be characterized logically by means of a suitable modal logic, called N…
A decidability proof for bisimulation equivalence of first-order grammars is given. It is an alternative proof for a result by Sénizergues (1998, 2005) that subsumes his affirmative solution of the famous decidability question for deterministic pushdown automata. The presented proof is conceptually simpler, and a particular novelty is that it is not given as two semidecision procedures but it provides an explicit algorithm that might be amenable to a complexity analysis.
