Strong Bisimilarity Research Articles

Coherent modal transition systems refinement

Modal Transition Systems (MTS) are a well-known formalism that extend Labelled Transition Systems (LTS) with the possibility of specifying necessary and permitted behaviour. Coherent MTS (CMTS) have been introduced to model Software Product Lines (SPL) based on a correspondence between the necessary and permitted modalities of MTS transitions and their associated actions, and the core and optional features of SPL. In this paper, we address open problems of the coherent fragment of MTS and introduce the notions of refinement and thorough refinement of CMTS. Most notably, we prove that refinement and thorough refinement coincide for CMTS, while it is known that this is not the case for MTS. We also define (thorough) equivalence and strong bisimilarity of both MTS and CMTS. We show their relations and, in particular, we prove that also strong bisimilarity and equivalence coincide for CMTS, whereas they do not for MTS. Finally, we extend our investigation to CMTS equipped with Constraints (MTSC), originally introduced to express alternative behaviour, and we prove that novel notions of refinement and strong thorough refinement coincide for MTSC, and so do their extensions to strong (thorough) equivalence and strong bisimilarity.

Linear parallel algorithms to compute strong and branching bisimilarity

We present the first parallel algorithms that decide strong and branching bisimilarity in linear time. More precisely, if a transition system has n states, m transitions and vert Act vert action labels, we introduce an algorithm that decides strong bisimilarity in mathcal {O}(n+vert Act vert ) time on max (n,m) processors and an algorithm that decides branching bisimilarity in mathcal {O}(n+vert Act vert ) time using up to max (n^2,m,vert Act vert n) processors.

Compositional equivalences based on open pNets

Establishing equivalences between programs is crucial both for verifying correctness of programs and for justifying optimisations and program transformations. There exist several equivalence relations for programs, and bisimulations are among the most versatile of these equivalences. Among bisimulations one distinguishes strong bisimulation that requires that each action of a program is simulated by a single action of the equivalent program, and weak bisimulation that allows some of the actions to be invisible, and thus not simulated.pNet is a generalisation of automata that model open systems. They feature variables and hierarchical composition. Open pNets are pNets with holes, i.e. placeholders that can be filled later by sub-systems. However, there is no standard tool for defining the semantics of an open system in this context. This article first defines open automata that are labelled transition systems with parameters and holes. Relying on open automata, it then defines bisimilarity relations for the comparison of systems specified as pNets. We first present a strong bisimilarity for open pNets called FH-bisimilarity. Next we offer an equivalence relation similar to the classical weak bisimulation equivalence, and study its properties. Among these properties we are interested in compositionality: if two systems are proven equivalent they will be indistinguishable by their context, and they will also be indistinguishable when their holes are filled with equivalent systems. We identify sufficient conditions to ensure compositionality of strong and weak bisimulation. The contributions of this article are illustrated using a transport protocol as running example.

Monadic compiler calculation (functional pearl)

Bahr and Hutton recently developed a new approach to calculating correct compilers directly from specifications of their correctness. However, the methodology only considers converging behaviour of the source language, which means that the compiler could potentially produce arbitrary, erroneous code for source programs that diverge. In this article, we show how the methodology can naturally be extended to support the calculation of compilers that address both convergent and divergent behaviour simultaneously , without the need for separate reasoning for each aspect. Our approach is based on the use of the partiality monad to make divergence explicit, together with the use of strong bisimilarity to support equational-style calculations, but also generalises to other forms of effect by changing the underlying monad.

Reactive bisimulation semantics for a process algebra with timeouts

This paper introduces the counterpart of strong bisimilarity for labelled transition systems extended with timeout transitions. It supports this concept through a modal characterisation, congruence results for a standard process algebra with recursion, and a complete axiomatisation.

On Decidability of the Bisimilarity on Higher-order Processes with Parameterization

Higher-order processes with parameterization are capable of abstraction and application (migrated from the lambda-calculus), and thus are computationally more expressive. For the minimal higher-order concurrency, it is well-known that the strong bisimilarity (i.e., the strong bisimulation equality) is decidable in absence of parameterization. By contrast, whether the strong bisimilarity is still decidable for parameterized higher-order processes remains unclear. In this paper, we focus on this issue. There are basically two kinds of parameterization: one on names and the other on processes. We show that the strong bisimilarity is indeed decidable for higher-order processes equipped with both kinds of parameterization. Then we demonstrate how to adapt the decision approach to build an axiom system for the strong bisimilarity. On top of these results, we provide an algorithm for the bisimilarity checking.

Distribution Bisimilarity via the Power of Convex Algebras

Probabilistic automata (PA), also known as probabilistic nondeterministic labelled transition systems, combine probability and nondeterminism. They can be given different semantics, like strong bisimilarity, convex bisimilarity, or (more recently) distribution bisimilarity. The latter is based on the view of PA as transformers of probability distributions, also called belief states, and promotes distributions to first-class citizens. We give a coalgebraic account of distribution bisimilarity, and explain the genesis of the belief-state transformer from a PA. To do so, we make explicit the convex algebraic structure present in PA and identify belief-state transformers as transition systems with state space that carries a convex algebra. As a consequence of our abstract approach, we can give a sound proof technique which we call bisimulation up-to convex hull.

Bisimulation and bisimilarity for fuzzy description logics under the Gödel semantics

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 interpretation. In DLs and their fuzzy extensions, such equivalence relations can be used for concept learning. In this paper, we define and study fuzzy bisimulation and bisimilarity for fuzzy DLs under the Gödel semantics, as well as crisp bisimulation and strong bisimilarity for such logics extended with involutive negation. The considered logics are fuzzy extensions of the DL ALCreg (a variant of PDL) with additional features among inverse roles, nominals, (qualified or unqualified) number restrictions, the universal role, local reflexivity of a role and involutive negation. We formulate and prove results on invariance of concepts under fuzzy (resp. crisp) bisimulation, conditional invariance of fuzzy TBoxes/ABoxes under bisimilarity (resp. strong bisimilarity), and the Hennessy-Milner property of fuzzy (resp. crisp) bisimulation for fuzzy DLs without (resp. with) involutive negation under the Gödel semantics. Apart from these fundamental results, we also provide results on using fuzzy bisimulation to separate the expressive powers of fuzzy DLs, as well as results on using strong bisimilarity to minimize fuzzy interpretations.

An Axiomatization for Quantum Processes to Unifying Quantum and Classical Computing

We establish an axiomatization for quantum processes, which is a quantum generalization of process algebra ACP (Algebra of Communicating Processes). We use the framework of a quantum process configuration 〈p, ϱ〉, but we treat it as two relative independent part: the structural part p and the quantum part ϱ, because the establishment of a sound and complete theory is dependent on the structural properties of the structural part p. We let the quantum part ϱ be the outcomes of execution of p to examine and observe the function of the basic theory of quantum mechanics. We establish not only a strong bisimilarity for quantum processes, but also a weak bisimilarity to model the silent step and abstract internal computations in quantum processes. The relationship between quantum bisimilarity and classical bisimilarity is established, which makes an axiomatization of quantum processes possible. An axiomatization for quantum processes called qACP is designed, which involves not only quantum information, but also classical information and unifies quantum computing and classical computing. qACP can be used easily and widely for verification of most quantum communication protocols.

A formal approach to open multiparty interactions

We present a process algebra aimed at describing interactions that are multiparty, i.e. that may involve more than two processes and that are open, i.e. the number of the processes they involve is not fixed or known a priori. Here we focus on the theory of a core version of a process calculus, without message passing, called Core Network Algebra (CNA). In CNA communication actions are given not in terms of channels but in terms of chains of links that record the source and the target ends of each hop of interactions. The operational semantics of our calculus mildly extends the one of CCS. The abstract semantics is given in the style of bisimulation but requires some ingenuity. Remarkably, the abstract semantics is a congruence for all operators of CNA and also with respect to substitutions, which is not the case for strong bisimilarity in CCS. As a motivating and running example, we illustrate the model of a simple software defined network infrastructure.

Unique Parallel Decomposition for the Pi-calculus

A (fragment of a) process algebra satisfies unique parallel decomposition if the definable behaviours admit a unique decomposition into indecomposable parallel components. In this paper we prove that finite processes of the pi-calculus, i.e. processes that perform no infinite executions, satisfy this property modulo strong bisimilarity and weak bisimilarity. Our results are obtained by an application of a general technique for establishing unique parallel decomposition using decomposition orders.

Timed process calculi with deterministic or stochastic delays: Commuting between durational and durationless actions

Several deterministically/stochastically timed process calculi have been proposed in the literature that, apart from their synchronization mechanism, mainly differ for the way in which actions and delays are represented. In particular, a distinction is made between integrated-time calculi, in which actions are durational, and orthogonal-time calculi, in which actions are instantaneous and delays are expressed separately. In a previous work on deterministic time, the two approaches have been shown to be reconcilable through an encoding from the integrated-time calculus CIPA to the orthogonal-time calculus TCCS, which preserves strong timed bisimilarity under certain conditions. In this paper, the picture is completed by first defining a reverse encoding from TCCS to CIPA, which requires slight modifications to both calculi and is shown to preserve only weak timed bisimilarity under conditions tighter than those for the direct encoding. Stochastic time is then addressed, by exhibiting an encoding from the integrated-time calculus MTIPP to the orthogonal-time calculus IML, together with a reverse encoding requiring slight modifications only to the former calculus, with both encodings being shown to preserve strong Markovian bisimilarity under suitable conditions. All the four encodings rely on the assumption that action execution is urgent. Variants are finally discussed in which action execution is delayable, in the sense that an enabled action can let time advance before starting its execution, or only the execution of internal actions is urgent, which is known as maximal progress.

Product line process theory

Software product lines (SPLs) facilitate reuse and customization in software development by genuinely addressing the concept of variability. Product Line Calculus of Communicating Systems (PL-CCS) is a process calculus for behavioral modeling of SPLs, in which variability can be explicitly modeled by a binary variant operator. In this paper, we study different notions of behavioral equivalence for PL-CCS, based on Park and Milner's strong bisimilarity. These notions enable reasoning about the behavior of SPLs at different levels of abstraction. We study the compositionality property of these notions and the mutual relationship among them. We further show how the strengths of these notions can be consolidated in an equational reasoning method. Finally, we designate the notions of behavioral equivalence that are characterized by the property specification language for PL-CCS, called multi-valued modal μ-calculus.

Weak CCP bisimilarity with strong procedures

Concurrent constraint programming (CCP) is a well-established model for concurrency that singles out the fundamental aspects of asynchronous systems whose agents (or processes) evolve by posting and querying (partial) information in a global medium. Bisimilarity is a standard behavioral equivalence in concurrency theory. However, only recently a well-behaved notion of bisimilarity for CCP, and a CCP partition refinement algorithm for deciding the strong version of this equivalence have been proposed. Weak bisimilarity is a central behavioral equivalence in process calculi and it is obtained from the strong case by taking into account only the actions that are observable in the system. Typically, the standard partition refinement can also be used for deciding weak bisimilarity simply by using Milner's reduction from weak to strong bisimilarity; a technique referred to as saturation. In this paper we demonstrate that, because of its involved labeled transitions, the above-mentioned saturation technique does not work for CCP. We give an alternative reduction from weak CCP bisimilarity to the strong one that allows us to use the CCP partition refinement algorithm for deciding this equivalence.

A procedure for splitting data-aware processes and its application to coordination

We present a procedure for splitting processes in a process algebra with multiactions and data (the untimed subset of the specification language mCRL2). This splitting procedure cuts a process into two processes along a set of actions A: roughly, one of these processes contains no actions from A, while the other process contains only actions from A. We state and prove a theorem asserting that the parallel composition of these two processes is provably equal from a set of axioms (sound and complete with respect to strong bisimilarity) to the original process under some appropriate notion of synchronization.We apply our splitting procedure to the process algebraic semantics of the coordination language Reo: using this procedure and its related theorem, we formally establish the soundness of splitting Reo connectors along the boundaries of their (a)synchronous regions in implementations of Reo. Such splitting can significantly improve the performance of connectors as shown elsewhere.

Algebraic Meta-Theory of Processes with Data

There exists a rich literature of rule formats guaranteeing different algebraic properties for formalisms with a Structural Operational Semantics. Moreover, there exist a few approaches for automatically deriving axiomatizations characterizing strong bisimilarity of processes. To our knowledge, this literature has never been extended to the setting with data (e.g. to model storage and memory). We show how the rule formats for algebraic properties can be exploited in a generic manner in the setting with data. Moreover, we introduce a new approach for deriving sound and ground-complete axiom schemata for a notion of bisimilarity with data, called stateless bisimilarity, based on intuitive auxiliary function symbols for handling the store component. We do restrict, however, the axiomatization to the setting where the store component is only given in terms of constants.

Evaluating functions as processes

A famous result by Milner is that the lambda-calculus can be simulated inside the pi-calculus. This simulation, however, holds only modulo strong bisimilarity on processes, i.e. there is a slight mismatch between beta-reduction and how it is simulated in the pi-calculus. The idea is that evaluating a lambda-term in the pi-calculus is like running an environment-based abstract machine, rather than applying ordinary beta-reduction. In this paper we show that such an abstract-machine evaluation corresponds to linear weak head reduction, a strategy arising from the representation of lambda-terms as linear logic proof nets, and that the relation between the two is as tight as it can be. The study is also smoothly rephrased in the call-by-value case, introducing a call-by-value analogous of linear weak head reduction.

Reducing Weak to Strong Bisimilarity in CCP

Concurrent constraint programming (ccp) is a well-established model for concurrency that singles out the fundamental aspects of asynchronous systems whose agents (or processes) evolve by posting and querying (partial) information in a global medium. Bisimilarity is a standard behavioural equivalence in concurrency theory. However, only recently a well-behaved notion of bisimilarity for ccp, and a ccp partition refinement algorithm for deciding the strong version of this equivalence have been proposed. Weak bisimiliarity is a central behavioural equivalence in process calculi and it is obtained from the strong case by taking into account only the actions that are observable in the system. Typically, the standard partition refinement can also be used for deciding weak bisimilarity simply by using Milner's reduction from weak to strong bisimilarity; a technique referred to as saturation. In this paper we demonstrate that, because of its involved labeled transitions, the above-mentioned saturation technique does not work for ccp. We give an alternative reduction from weak ccp bisimilarity to the strong one that allows us to use the ccp partition refinement algorithm for deciding this equivalence.

Results on Embeddings Between State-Based and Event-Based Systems

Kripke Structures (KSs) and Labelled Transition Systems (LTSs) are the two most prominent semantic models used in concurrency theory. Both models are commonly believed to be equi-expressive. One can find manyad hoc embeddings of one of these models into the other. We build upon the seminal work of De Nicola and Vaandrager that firmly established the correspondence between stuttering equivalence in KSs and divergence-sensitive branching bisimulation in LTSs. We show that their embeddings can also be used for a range of other equivalences of interest, such as strong bisimilarity, simulation equivalence and trace equivalence. Furthermore, we extend the results by De Nicola and Vaandrager by showing that there are additional translations that allow one to use minimization techniques in one semantic domain to obtain minimal representatives in the other semantic domain for these equivalences.

Axiomatizing GSOS with Predicates

In this paper, we introduce an extension of the GSOS rule format with predicates such as termination, convergence and divergence. For this format we generalize the technique proposed by Aceto, Bloom and Vaandrager for the automatic generation of ground-complete axiomatizations of bisimilarity over GSOS systems. Our procedure is implemented in a tool that receives SOS specifications as input and derives the corresponding axiomatizations automatically. This paves the way to checking strong bisimilarity over process terms by means of theorem-proving techniques.