Calculus Of Communicating Systems Research Articles

Formalizing CCS and π-calculus in Guarded Cubical Agda

Dependent type theories with guarded recursion have shown themselves suitable for the development of denotational semantics of programming languages. In particular, Ticked Cubical Type Theory (TCTT) has been used to show that, for guarded labeled transition systems (GLTS), interpretation into the denotational semantics maps bisimilar processes to equal values. In fact the two notions are proved equivalent, allowing one to reason about equality in place of bisimilarity.We extend that result to the Calculus of Communicating Systems (CCS) and the π-calculus. For the latter, we pick early congruence as the syntactic notion of equivalence between processes, showing that denotational models based on guarded recursive types can handle the dynamic creation of channels that goes beyond the scope of GLTSs.Hence we present fully abstract denotational models for CCS and the early π-calculus, formalized as an extended example for Guarded Cubical Agda: a novel implementation of Ticked Cubical Type Theory based on Cubical Agda.

Verification of the Instantiation and Integration of Security Patterns

As software applications suffer from increasing malicious attacks, security becomes a critically important issue for software development. To avoid security problems and increase efficiency, a large software system design may reuse good security solutions for existing security patterns. While security patterns document expert solutions to common security problems and capture well-examined practices on secure software design, implementing them in a particular context (pattern instantiation) and composing them with other related patterns (pattern integration) are prone to flaws and may break expected security properties. In this paper, we present an approach to verify security patterns instantiation and integration automatically. We offer formal definitions for security pattern instantiation and integration, and establish rules to transform sequence diagrams (representing the behaviors of security patterns) to expressions in Milner’s Calculus of Communicating Systems (CCS). We prove the correctness of the proposed transformation, and propose an algorithm to carry out this transformation automatically. In particular, we formally specify the alternative flows of UML sequence diagrams guarded by constraint conditions, which allows us to model choice making behaviors of security patterns precisely. The properties of the instantiation and integration can be verified by model checking against their CCS expressions. Flaws of instantiation and integration can, therefore, be discovered early in the design stage. We use two case studies to illustrate our approach and show the capability to prove security in integration and detect design errors in instantiation respectively.

Unique solutions of contractions, CCS, and their HOL formalisation

The unique solution of contractions is a proof technique for (weak) bisimilarity that overcomes certain syntactic limitations of Milner's “unique solution of equations” theorem. This paper presents an overview of a comprehensive formalisation of Milner's Calculus of Communicating Systems (CCS) in the HOL theorem prover (HOL4), with a focus towards the theory of unique solutions of equations and contractions. The formalisation consists of about 24,000 lines (1MB) of code in total. Some refinements of the “unique solution of contractions” theory itself are obtained. In particular we remove the constraints on summation, which must be guarded, by moving from contraction to rooted contraction. We prove the “unique solution of rooted contractions” theorem and show that rooted contraction is the coarsest precongruence contained in the contraction preorder.

A calculus of concurrent graph-rewriting processes

State-of-the-art approaches to controlled graph rewriting focus on the specification of an external control layer over graph-rewriting rule applications and on the input-output semantics of the resulting systems, leading to a decreased relevance of many interesting operational aspects of graph transformation, as studied in the classical theory of algebraic graph rewriting.We propose a novel approach to controlled graph rewriting where we aim at bridging the gap between these two complementary approaches, defining an operational semantics for which classical concepts and results related to independence and parallelism of graph derivations can be recast.The calculus we propose is based on a control layer specified using (a fragment of) Milner's Calculus of Communicating Systems (CCS), where the actions specify the application of graph transformation rules to the current state, according to the Double-Pushout approach (DPO).In particular, we address the following aspects for our controlled graph-rewriting processes: (i) expressiveness of the control language, compared to a minimally complete reference language, Graph Programs, proposed by Habel and Plump; (ii) process equivalence based on labeled transition systems and a structural operational semantics; (iii) a unifying treatment of action independence, considering the corresponding notions from both process algebra and graph-rewriting theory; and (iv) parallelism and concurrency based on the notion of asynchronous (labeled) transition systems, obtained from an asynchronous version of the proposed calculus.

An Interpretation of CCS into Ludics

Starting from works aimed at extending the Curry-Howard correspondence to process calculi through linear logic, we give another Curry-Howard counterpart for Milner's Calculus of Communicating Systems (CCS) by taking Ludics as the target system. Indeed interaction, Ludics' dynamic, allows to fully represent both the non-determinism and non-confluence of the calculus.We give an interpretation of CCS processes into carefully defined behaviours of Ludics using a new construction, called directed behaviour, that allows controlled interaction paths by using pruned designs. We characterize the execution of processes as interaction on behaviours, by implicitly representing the causal order and conflict relation of event structures. As a direct consequence, we are also able to interpret deadlocked processes, and identify deadlock-free ones.

Analysing Mutual Exclusion using Process Algebra with Signals

In contrast to common belief, the Calculus of Communicating Systems (CCS) and similar process algebras lack the expressive power to accurately capture mutual exclusion protocols without enriching the language with fairness assumptions. Adding a fairness assumption to implement a mutual exclusion protocol seems counter-intuitive. We employ a signalling operator, which can be combined with CCS, or other process calculi, and show that this minimal extension is expressive enough to model mutual exclusion: we confirm the correctness of Peterson's mutual exclusion algorithm for two processes, as well as Lamport's bakery algorithm, under reasonable assumptions on the underlying memory model. The correctness of Peterson's algorithm for more than two processes requires stronger, less realistic assumptions on the underlying memory model.

Teaching Formal Models of Concurrency Specification and Analysis

There is a widespread and rapidly growing interest to the parallel programming nowadays. This interest is based on availability of supercomputers, computer clusters and powerful graphic processors for computational mathematics and simulation. MPI, OpenMP, CUDA and other technologies provide opportunity to write C and FORTRAN code for parallel speed-up of execution without races for resources. Nevertheless concurrency issues (like races) are still very important for parallel systems in general and distributed systems in particular. Due to this reason, there is a need of research, study and teaching of formal models of concurrency and methods of distributed system verification. The paper presents an individual experience with teaching Formal Models of Concurrency as a graduate elective course for students specializing in high-performance computing. First it sketches course background, objectives, lecture plan and topics. Then the paper presents how to formalize (i.e. specify) a reachability puzzle in semantic, syntactic and logic formal models, namely: in Petri nets, in a dialect of Calculus of Communicating Systems (CCS) and in Computation Tree Logic (CTL). This puzzle is a good educational example to present specifics of different formal notations. The article is published in the author’s wording.

프로세스 유사도 분석과 메타 저장소를 이용한 서비스 재사용 기법

클라우드 컴퓨팅에서 SaaS는 소프트웨어를 서비스로서 제공하는 프레임워크이다. 테넌트와 용도의 차이에 따라 서비스 제공자가 서비스를 다시 구축한다면 비용이나 관리적 측면에서 많은 자원을 요구하게 된다. 이에 우리는 기존 소프트웨어를 재사용 할 수 있도록 프로세스 알제브라를 이용하여 분석하는 기법을 제안한다. process algebra는 소프트웨어의 구조를 분석하고, 이를 다른 언어로 표현할 수 있으며, 재사용할 수 있는지 검증할 수 있다. process algebra 중 CCS(Calculus of Communicating Systems)는 비즈니스 프로세스나 XML로 변환하기 유용하므로, 이를 이용하여 프로세스를 프로세스 뷰로 구조화하고, 구조화된 명세를 비교 및 관리를 위한 메타 저장소를 제안한다. SaaS at a cloud computing is a framework to provide a software as a service. Depending on the difference of the tenant and the use, if the service provider re-establish a service, they are required resources In terms of costs and managerial. So we propose a technique for analysis of software structure using the process algebra to reuse existing software. A process algebra analyze the structure of the software, express in different languages and verify that it can be reused. CCS in a process algebra is useful to convert the business process or XML, by using this, we structure a process as process view and propose meta storage for comparison and management a structured document.

CD-Form: A clone detector based on formal methods

This paper presents the design and implementation of CD-Form (Clone Detector based on FORmal Methods), a tool targeted at the detection of Type-2 clones in Java code. CD-Form is based on a novel approach for detecting code clones. The methodology adopted performs the analysis on Java bytecode and not on the original Java source. The bytecode is transformed into CCS (Calculus of Communicating Systems) processes, which are successively checked for equivalence. After a thorough description of the methodology used for detecting clones, the design of the tool is presented. The results obtained by evaluating sample Java codes are validated by comparing them to those obtained by a state-of-the-art tool for clone detection.

Structured Operational Semantics for Graph Rewriting

Process calculi and graph transformation systems provide models of reactive systems with labelled transition semantics. While the semantics for process calculi is compositional, this is not the case for graph transformation systems, in general. Hence, the goal of this article is to obtain a compositional semantics for graph transformation system in analogy to the structural operational semantics (SOS) for Milner's Calculus of Communicating Systems (CCS). The paper introduces an SOS style axiomatization of the standard labelled transition semantics for graph transformation systems. The first result is its equivalence with the so-called Borrowed Context technique. Unfortunately, the axiomatization is not compositional in the expected manner as no rule captures "internal" communication of sub-systems. The main result states that such a rule is derivable if the given graph transformation system enjoys a certain property, which we call "complementarity of actions". Archetypal examples of such systems are interaction nets. We also discuss problems that arise if "complementarity of actions" is violated.

Combinatorics of labelling in higher-dimensional automata

The main idea for interpreting concurrent processes as labelled precubical sets is that a given set of n actions running concurrently must be assembled to a labelled n -cube, in exactly one way. The main ingredient is the non-functorial construction called the labelled directed coskeleton. It is defined as a subobject of the labelled coskeleton, the latter coinciding in the unlabelled case with the right adjoint to the truncation functor. This non-functorial construction is necessary since the labelled coskeleton functor of the category of labelled precubical sets does not fulfil the above requirement. We prove in this paper that it is possible to force the labelled coskeleton functor to be well behaved by working with labelled transverse symmetric precubical sets. Moreover, we prove that this solution is the only one. A transverse symmetric precubical set is a precubical set equipped with symmetry maps and with a new kind of degeneracy map called transverse degeneracy. Finally, we also prove that the two settings are equivalent from a directed algebraic topological viewpoint. To illustrate, a new semantics of the calculus of communicating systems (CCS), equivalent to the old one, is given.

On Process Equivalence = Equation Solving in CCS

Unique Fixpoint Induction (UFI) is the chief inference rule to prove the equivalence of recursive processes in the Calculus of Communicating Systems (CCS) (Milner 1989). It plays a major role in the equational approach to verification. Equational verification is of special interest as it offers theoretical advantages in the analysis of systems that communicate values, have infinite state space or show parameterised behaviour. We call these kinds of systems VIPSs. VIPSs is the acronym of Value-passing, Infinite-State and Parameterised Systems. Automating the application of UFI in the context of VIPSs has been neglected. This is both because many VIPSs are given in terms of recursive function symbols, making it necessary to carefully apply induction rules other than UFI, and because proving that one VIPS process constitutes a fixpoint of another involves computing a process substitution, mapping states of one process to states of the other, that often is not obvious. Hence, VIPS verification is usually turned into equation solving (Lin 1995a). Existing tools for this proof task, such as VPAM (Lin 1993), are highly interactive. We introduce a method that automates the use of UFI. The method uses middle-out reasoning (Bundy et al. 1990a) and, so, is able to apply the rule even without elaborating the details of the application. The method introduces meta-variables to represent those bits of the processes' state space that, at application time, were not known, hence, changing from equation verification to equation solving. Adding this method to the equation plan developed by Monroy et al. (Autom Softw Eng 7(3):263---304, 2000a), we have implemented an automatic verification planner. This planner increases the number of verification problems that can be dealt with fully automatically, thus improving upon the current degree of automation in the field.

Reachability Analysis of Variants of Communication-Free Petri Nets

Communication-free Petri nets provide a net semantics for Basic Parallel Processes, which form a subclass of Milner's Calculus of Communicating Systems (CCS) a process calculus for the description and algebraic manipulation of concurrent communicating systems. It is known that the reachability problem for communication-free Petri nets is NP-complete. Lacking the synchronization mechanism, the expressive power of communication-free Petri nets is somewhat limited. It is therefore importance to see whether the power of communication-free Petri nets can be enhanced without sacrificing their analytical capabilities. As a first step towards this line of research, in this paper our main concern is to investigate, from the decidability/complexity viewpoint, the reachability problem for a number of variants of communication-free Petri nets, including communication-free Petri nets augmented with ‘static priorities, ’ ‘dynamic priorities, ’ ‘states, ’ ‘inhibitor arcs, ’ and ‘timing constraints.’

Expressing First-Order π-Calculus in Higher-Order Calculus of Communicating Systems

In the study of process calculi, encoding between different calculi is an effective way to compare the expressive power of calculi and can shed light on the essence of where the difference lies. Thomsen and Sangiorgi have worked on the higher-order calculi (higher-order Calculus of Communicating Systems (CCS) and higher-order π-calculus, respectively) and the encoding from and to first-order π-calculus. However a fully abstract encoding of first-order π-calculus with higher-order CCS is not available up-today. This is what we intend to settle in this paper. We follow the encoding strategy, first proposed by Thomsen, of translating first-order π-calculus into Plain CHOCS. We show that the encoding strategy is fully abstract with respect to early bisimilarity (first-order π-calculus) and wired bisimilarity (Plain CHOCS) (which is a bisimulation defined on wired processes only sending and receiving wires), that is the core of the encoding strategy. Moreover from the fact that the wired bisimilarity is contained by the well-established context bisimilarity, we secure the soundness of the encoding, with respect to early bisimilarity and context bisimilarity. We use index technique to get around all the technical details to reach these main results of this paper. Finally, we make some discussion on our work and suggest some future work.

Formal Verification of Concurrent Systems via Directed Model Checking

Model checking suffers from the state explosion problem, due to the exponential increase in the size of a finite state model as the number of system components grows. Directed model checking aims at reducing this problem through heuristic-based search strategies. The model of the system is built while checking the formula and this construction is guided by some heuristic function. In this line, we have defined a structure-based heuristic function operating on processes described in the Calculus of Communicating Systems (CCS), which accounts for the structure of the formula to be verified, expressed in the selective Hennessy-Milner logic. We have implemented a tool to evaluate the method and verified a sample of well known CCS processes with respect to some formulae, the results of which are reported and commented.

A bulk-synchronous parallel process algebra

The calculus of communicating systems (CCS) process algebra is a well-known formal model of synchronization and communication. It is used for the analysis of safety and liveness in protocols or distributed programs. In more recent work, it is used for the analysis of security properties. Bulk-synchronous parallelism (BSP) is an algorithm and programming model of data-parallel computation. It is useful for the design, analysis and programming of scalable parallel algorithms. Many current evolutions require the integration of distributed and parallel programming: grid systems for sharing resources across the Internet, secure and reliable global access to parallel computer systems, geographic distribution of confidential data on randomly accessible systems, etc. Such software services must provide guarantees of safety, liveness, security together with scalable and reliable performance. Formal models are therefore needed to combine parallel performance and concurrent behavior. With this goal in mind, we propose here an integration of BSP with CCS semantics, generalize its cost (performance) model and sketch its application to scheduling problems in meta-computing.

Formalising Workflow: A CCS-inspired Characterisation of the YAWL Workflow Patterns

We present work concerning the formal specification of business processes. It is of substantial benefit to be able to pin down the meaning of business processes precisely. This is an end in itself, but we are also concerned to do so in order that we might prove properties about the business processes that are being specified. It is a notable characteristic of most languages for representing business processes that they lack a robust semantics, and a notable characteristic of most commercial Business Process Management products that they have no support for verification of business process models. We define a high-level meta-model, called Liesbet , for representing business processes. The ontological commitments for Liesbet are sourced from the YAWL workflow patterns, which have been defined from studies into the behavioural nature of business processes. A formal characterisation of Liesbet is provided using Milner’s Calculus of Communicating Systems (CCS). In this article, we omit some of the technical details of this characterisation and instead present the essential features by means of an abstract machine language, called LCCS. We also explain how we have facilitated the verification of certain properties of business processes specified in Liesbet , and discuss how Liesbet supports the YAWL workflow patterns. We include a simple three-part example of using Liesbet .

Behavioural equivalence in simulation modelling

Discrete event simulation has grown up as a practical technique for estimating the quantitative behaviour of systems, where direct measurement is undesirable or impractical. It is also used to understand the detailed functional behaviour of such systems. Its theory is largely that of experimental science, centering on statistical approaches to validation, rather than on the verification of detailed behaviour. On the other hand, much work has been done on understanding and proving functional properties of systems, using techniques of formal specification and concurrency modelling. This article presents an approach to understanding equivalence of behaviour of discrete event simulation models, using a technique from the concurrency world, Milner’s Calculus of Communicating Systems (CCS). This yields a significant advance over the main previous work, Schruben and Yücesan’s simulation graphs. CCS allows for the use of observational equivalence, which can capture a more flexible, behavioural notion of equivalence than the structural equivalence defined there. A common framework based on the process view of models is constructed, using a hierarchical graphical modelling language (Extended Activity Diagrams). This language is shown to map onto both the major constructs of the DEMOS discrete event simulation language and the corresponding CCS models. A graphically driven tool based on such a framework is presented, which generates both types of models. Using the CCS model, behavioural equivalences and differences in simulation models are demonstrated.

Modelling, property verification and behavioural equivalence of lactose operon regulation

Understanding biochemical pathways is one of the biggest challenges in the field of molecular biology nowadays. Computer science can contribute in this area by providing formalisms and tools to simulate and analyse pathways. One formalism that is suited for modelling concurrent systems is Milner's Calculus of Communicating Systems (CCS). This paper shows the viability of using CCS to model and reason about biochemical networks. As a case study, we describe the regulation of lactose operon. After describing this operon formally using CCS, we validate our model by automatically checking some known properties for lactose regulation. Moreover, since biological systems tend to be very complex, we propose to use multiple descriptions of the same system at different levels of abstraction. The compatibility of these multiple views can be assured via mathematical proofs of observational equivalence.

A structured operational semantic modelling of the Dolev–Yao threat environment and its composition with cryptographic protocols

In the areas of computer security and cryptographic protocols a standard model for describing the malicious behaviour of adversaries is the Dolev–Yao threat model. In formal analysis of complex, reactive and concurrent communication systems, a well-researched algebraic process approach is Milner's Calculus of Communicating Systems (CCS) which has the semantic foundation underpinned by Plotkin's structured operational semantics (SOS). In this article we provide a CCS-SOS modelling of the Dolev–Yao threat environment and its composition with the CCS description of a cryptographic protocol. For a given protocol, we attempt to discover security flaws by examining whether there is any difference between the SOS transition behaviours of the protocol descriptions which has and has not been composed with the malicious environment. The intuitively appealing modelling shows a suitability for the well-researched CCS-SOS-based algebraic process approach being applied to formal analysis of cryptographic protocols.