Milner's Calculus Research Articles

Non-functional requirements in the software development process

The satisfaction of a customer's non-functional requirements is an important factor in determining the acceptince of a designed system. They can be seen as constraints on either the final product or on the development process. Each such requirement may generate further constraints, depending on decisions taken, forming a graph, and a path can be traced between the original requirement and a design commitment. Work has been carried out on modelling where in the development process such decisions are best taken using Milner's Calculus of Communicating Systems, with agents representing roles and documents. A prototype support environment based on the model is being implemented using C and Motif.

Deciding bisimulation and trace equivalences for systems with many identical processes

In the study of process semantics, trace equivalence and bisimulation equivalence constitute the two extremes of the so-called linear time—branching time spectrum. In this paper, we study the complexity and decidability issues of deciding trace and bisimulation equivalences for the model of systems with many identical processes with respect to various interprocess communication structures. In our model, each system consists of an arbitrary number of identical finite-state processes using Milner's calculus of communicating systems (CCS) as the style of interprocess communication. As it turns out, deciding trace and bisimulation equivalences are undecidable for star-like and linear systems, whereas the two problems are complete for PSPACE and PTIME, respectively, for fully connected systems.

Petri-net-based deadlock analysis of Process Algebra programs

Recent research has been conducted on representing Process Algebra programs by safe Petri nets. We suggest that such a representation offers direct benefits: one can use methods that have been developed in the Petri net theory domain, to reason about Process Algebra programs. We propose for a subset of a specific Process Algebra (Milner's Calculus of Communicating Systems or CCS), a deadlock detection algorithm which is based on Petri net reduction techniques. The Petri net model of a CCS program is transformed into a simpler one which contains a smaller number of states, without losing however any deadlock information. An implementation of the proposed technique confirms that net-based verification of processes is a promising area of research.

The concurrency workbench

The Concurrency Workbench is an automated tool for analyzing networks of finite-state processes expressed in Milner's Calculus of Communicating Systems. Its key feature is its breadth: a variety of different verification methods, including equivalence checking, preorder checking, and model checking, are supported for several different process semantics. One experience from our work is that a large number of interesting verification methods can be formulated as combinations of a small number of primitive algorithms. The Workbench has been applied to the verification of communications protocols and mutual exclusion algorithms and has proven a valuable aid in teaching and research.

CCS expressions, finite state processes, and three problems of equivalence

We examine the computational complexity of testing finite state processes for equivalence in Milner's Calculus of Communicating Systems (CCS). The equivalence problems in CCS are presented as refinements of the familiar problem of testing whether two nondeterministic finite automata (NFA) are equivalent, i.e., accept the same language. Three notions of equivalence proposed for CCS are investigated, namely, observational equivalence, strong observational equivalence , and failure equivalence . We show that observational equivalence can be tested in polynomial time. As defined in CCS, observational equivalence is the limit of a sequence of successively finer equivalence relations, ≈ k , where ≈ 1 is nondeterministic finite automaton equivalence. We prove that, for each fixed k , deciding ≈ k is PSPACE-complete. We show that strong observational equivalence can be decided in polynomial time by reducing it to generalized partitioning , a new combinatorial problem of independent interest. Finally, we demonstrate that testing for failure equivalence is PSPACE-complete, even for a very restricted type of process.

Bisimulation and divergence

Behavioural preorders based on the idea of bisimulation but refining the notion of bisimulation equivalence and providing explicit treatments of the phenomenon of divergence in communicating systems are investigated. Particular study is made of these preorders in the context of Milner's Calculus of Communicating Systems. The precongruence relations generated by the preorders are characterized and axiomatized on the classes of finite closed terms and sequential terms. A verification technique based on the theory of the preorders is introduced and illustrated.

Type theory and concurrency

This paper describes the use of an automated reasoning tool, the Nuprl system, to formalize Milner's Calculus of Communicating Systems (CCS). The goals of this work are two-fold: the first is to investigate the feasibility of using systems like Nuprl to handle the formal detail arising from reasoning about concurrency, while the second is to develop a framework in which various formalisms for reasoning about concurrency may be presented in an automated fashion. To these ends, an implementation in Nuprl of a formal theory of concurrency is described, an implementation of CCS in this mechanized semantic theory presented, and two means of analyzing CCS terms are investigated.

An interpreter for LOTOS, a specification language for distributed systems

AbstractLOTOS is an executable specification language for distributed systems currently being standardized within ISO as a tool for the formal specification of open systems interconnection protocols and services. It is based on an extended version of Milner's calculus of communicating systems (CCS) and on ACT ONE abstract data type (ADT) formalism. A brief introduction to LOTOS is given, along with a discussion of LOTOS operational semantics, and of the executability of LOTOS specifications. Further, an account of a prototype LOTOS interpreter is given, which includes an interactive system that allows the user to direct the execution of a specification (for example, for testing purposes). The interpreter was implemented in YACC/LEX, C and Prolog. The following topics are discussed: syntax and static semantics analysis; translation from LOTOS external format to internal representation; evaluation of ADT value expressions and extended CCS behaviour expressions. It is shown that the interpreter can be used in a variety of ways: to recognize whether a given sequence of interactions is allowed by the specification; to generate randomly chosen sequences of interactions; in a user‐guided generation mode, etc.

Broadcasting buffering communication

A language is suggested for representing broadcasting buffering communicating (BBC) systems. In contrast to hand shaking communication following the rendezvous-concept the language describes loosely coupled communicating systems. Both mathematical and operational semantics are defined and several issues of the language are discussed. In particular the relationship to Milner's calculus of communicating systems, Hoare's communicating sequential processes and Church's lambda-calculus is briefly investigated.

Extensions to communicating sequential processes to allow protocol performance specification

Formalisms based on Hoare's Communicating Sequential Processes (CSP) and Milner's Calculus of Communicating Systems (CCS) for verifying protocols are currently being used by the International Standard Organisation (ISO). However, these models need to be extended if protocol performance specification and verification is to be done, as neither of these models have timing information (other than sequencing) nor a way of specifying controlled loss of information. This paper presents two extensions to Hoare's CSP that are felt by the author to provide suitable mechanisms for specifying protocol performance. Firstly, the effects of introducing time into CSP are presented, based on the work done by Reed and Roscoe. Secondly, the traces model is modified by associating probabilities with event sequences. Finally, some example specifications are given using these two extensions.

Petri nets, algebras, morphisms, and compositionality

It is shown how a category of Petri nets can be viewed as a subcategory of two sorted algebras over multisets. This casts Petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition—the morphisms here respect the behaviour of nets. The categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components; for example, various forms of parallel composition of Petri nets arise naturally from the product in the category. This abstract setting makes plain a useful functor from the category of Petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of Petri nets—for instance, the coloured and higher level nets of Kurt Jensen arise through a simple modification of the sorts of the algebras underlying nets. Further, it provides a smooth formal relation with other models of concurrency such as Milner's calculus of communicating systems (CCS) and Hoare's communicating sequential processes (CSP), though this is only indicated in this paper.

Structure of a LOTOS interpreter

LOTOS is an executable specification language for protocols and services currently being standardized within ISO. It is based on an extended version of Milner's Calculus of Communicating Systems (CCS) and ACT ONE Abstract Data Type formalism. After a brief introduction to LOTOS, we give here an account of a prototype LOTOS interpreter, which includes an interactive system that allows the user to direct the execution of a specification. The interpreter was implemented in YACC/LEX, C, and Prolog. The discussion includes the following topics: syntax and static semantics analysis; translation from LOTOS external format to internal representation; evaluation of Abstract Data Type value expressions and CCS * clauses.

A Calculus of Communicating Systems with Label Passing

Milner's Calculus of Communicating Systems (CCS) is extended with a mechanism for label passing - as an attempt to remedy some of the shortcomings of CCS w.r.t. dynamic change of agent interconnections. In the extended calculus, restriction is viewed formally as a binder, and the calculus allows dynamic change of scope (of label) in connection with communication. It is proved that algebraic properties of strong (and observational) equivalence for CCS are preserved by the extension. Examples illustrating the expressive power of the calculus and its methods for reasoning are given.

Algebraic specification and verification of communication protocols

Assume a communication network, consisting of switching nodes which make connections (like telephone exchanges) and terminal nodes which use these connections (like subscribers, computer terminals, etc.). The terminal nodes are at the periphery of the network, whereas switching nodes are internal to the network. In this paper it is shown how Milner's calculus of communicating systems (CCS) can be applied to specify and verify the communication behaviour of switching nodes. Starting from a specification of the communication behaviour of terminal nodes, a specification for the protocol between terminal nodes and the network of switching nodes is systematically derived. In a similar way the communication behaviour of switching nodes inside the network is derived. Verification is based on a formal abstraction mechanism which shows the equivalence of a specification and the corresponding design. The expansion theorem of CCS, together with certain laws from CCS, provide such a mechanism. With these, it is proved that the behaviour of a network of switching nodes is observation equivalent to a single switching node, which proves the consistency of the specification of the communication behaviour of the network as a whole and the combined behaviour of its constituents, the switching nodes.

IDEOSY

IDEOSY is an experiment in the use of a formal semantics as the basis for a programming system and in use of an ideographic language as the primary means of user-computer communication. The important characteristics of our system are that it uses an ideographic syntax, has a syntax-directed editor, supports the definition of various equivalence properties and the proofs of such equivalence, and has an interpreter. It currently runs on Apollo workstations and on VAXes running Berkeley UNIX@ using any of a variety of high-resolution color displays. Our formalism is based on Milner's Calculus of Communicating Systems ( CCS ) [1]. We have found CCS to be a convenient formalism for describing programs and have even used it for describing the UNIX operating system [2]. Its algebraic properties are very useful for building descriptions out of components and for proving the equivalence of descriptions. Since CCS is an operational semantics, we may directly interpret descriptions written in CCS.

IDEOSY

IDEOSY is an experiment in the use of a formal semantics as the basis for a programming system and in use of an ideographic language as the primary means of user-computer communication. The important characteristics of our system are that it uses an ideographic syntax, has a syntax-directed editor, supports the definition of various equivalence properties and the proofs of such equivalence, and has an interpreter. It currently runs on Apollo workstations and on VAXes running Berkeley UNIX@ using any of a variety of high-resolution color displays. Our formalism is based on Milner's Calculus of Communicating Systems ( CCS ) [1]. We have found CCS to be a convenient formalism for describing programs and have even used it for describing the UNIX operating system [2]. Its algebraic properties are very useful for building descriptions out of components and for proving the equivalence of descriptions. Since CCS is an operational semantics, we may directly interpret descriptions written in CCS.

Processes and the denotational semantics of concurrency

A framework allowing a unified and rigorous definition of the semantics of concurrency is proposed. The mathematical model introduces processes as elements of process domains which are obtained as solutions of domain equations in the sense of Scott and Plotkin. Techniques of metric topology as proposed, e.g., by Nivat are used to solve such equations. Processes are then used as meanings of statements in languages with concurrency. Three main concepts are treated, viz. parallellism (arbitrary interleaving of sequences of elementary actions), synchronization, and communication. These notions are embedded in languages which also feature classical sequential concepts such as assignment, tests, iteration or recursion, and guarded commands. In the definitions, a sequence of process domains of increasing complexity is used. The languages discussed include Milner's calculus for communicating systems and Hoare's communicating sequential processes. The paper concludes with a section with brief remarks on miscellaneous notions in concurrency, and two appendices with mathematical details.