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Topic: Calculus of Communicating Systems

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	Amazon.com: Communicating and Mobile Systems: the Pi-Calculus: Books: Robin Milner (Site not responding. Last check: 2007-11-03)
		Communication is a fundamental and integral part of computing, whether between different computers on a network, or between components within a single computer.
		The pi-calculus is viewed as a `calculus of mobile processes.' Introduced in 1992 by the author, it views the movement of a process as due entirely to the movement of its links, i.e.
		The type systems he uses involve as expected the `sorts' and `sortings' that enable the classification of the sorts of information that can be transmitted in an interaction.
	www.amazon.com /Communicating-Mobile-Systems-Robin-Milner/dp/0521658691 (2322 words)

	Pi-calculus - Wikipedia, the free encyclopedia
		In theoretical computer science, the π-calculus is a process calculus originally developed by Robin Milner, Joachim Parrow and David Walker as a continuation of the body of work on the process calculus CCS (Calculus of Communicating Systems).
		Alternatively, one may give the pi-calculus a labelled transition semantics (as has been done with the Calculus of Communicating Systems).
		This polyadic extension can be encoded in the monadic calculus by passing the name of a private channel through which the multiple arguments are then passed in sequence.
	en.wikipedia.org /wiki/Pi-calculus (2293 words)

	Robin Milner
		Around 1980 he developed CCS (Calculus for Communicating Systems), one of the first algebraic calculi for analysing concurrent systems.
		In the late 1980s with two colleagues he devised the pi calculus, a basic model for mobile communicating systems.
		For over two decades the process calculus community has sought to combine two things: the way you define and analyze mobile distributed processes and the way you program them.
	www.fairdene.com /picalculus/robinmilner.html (2214 words)

	Calculus of Communicating Systems - Wikipedia, the free encyclopedia
		The Calculus of Communicating Systems (or CCS) is a process calculus developed by Robin Milner.
		What characterises our calculus is not the exact choice of combinators, but rather the choice of interpretation and of mathematical framework".
		The expressions of the language are interpreted as a labelled transition system.
	en.wikipedia.org /wiki/Calculus_of_Communicating_Systems (158 words)

	COM3190 Theory of Distributed Systems
		The aim of this module is to set out a strong theoretical basis for the analysis and design of concurrent and distributed systems, with particular emphasis on networks of mobile processes.
		The importance of mobile systems; pi-calculus specifications of a mobile phone system and unbounded, elastic buffers.
		Communicating and Mobile Systems: the pi-Calculus, Cambridge University Press, 1999.
	www.dcs.shef.ac.uk /intranet/teaching/modules/level3/com3190.html (593 words)

	Parallel/Distributed \| Lambda the Ultimate
		Semantics is done in terms of both a reduction system and a version of labelled transitions called commitment ; the known algebraic axiomatization of strong bisimilarity is given in the new setting, and so also is a characterization in modal logic....
		They use Scala's type system to reduce the burden of this restriction, however, since they're able to state that a particular statement never returns normally (and thus must not be followed by more statements).
		We prove that the type assignment system and the operational semantics of the calculus are ‘sound’, and we define a sound and complete type inference algorithm which, when applied to terms whose type decorations only express the desired policies, computes the minimal type annotations required for their execution.
	lambda-the-ultimate.org /taxonomy/term/16 (1696 words)

	Rance Cleaveland's Publications: 1989 (Site not responding. Last check: 2007-11-03)
		In this paper we show how the testing equivalences and preorders on transition systems may be interpreted as instances of generalized bisimulation equivalences and prebisimulation preorders.
		The characterization relies on defining transformations on the transition systems in such a way that the testing relations on the original systems correspond to (pre)bisimulation relations on the altered systems.
		Using these results, it is possible to use algorithms for determining the (pre)bisimulation relations in the case of finite-state transition systems to compute the testing relations.
	www.cs.umd.edu /~rance/publications/1989.html (388 words)

	Communicating and Mobile Systems - Cambridge University Press
		The calculus is very simple but powerful; its most prominent ingredient is the notion of a name.
		The internet, and its communication protocols, fall within the scope of the theory just as much as computer programs, data structures, algorithms and programming languages.
		This book is the first textbook on the subject; it has been long-awaited by professionals and will be welcomed by them, and their students.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521658691 (215 words)

	The Calculus of Communicating Systems
		CWB is capable of displaying a simulation of a concurrent system described in CCS, searching for deadlock states, testing for equality between two agents, and determining if a system satisfies a given logical property (e.g., safety or liveness).
		In a labelled transition system, the vertices in a directed graph represent CCS expressions (or agent states) and each arc is labelled by the event/action that causes the expression (state) from which the arc emmanates to become the expression (state) to which the arc is directed.
		That is, the system H allows outside agents to interact with it at any of its ports a,b,x or 'x.
	ei.cs.vt.edu /~cs5204/fall99/ccs.html (1616 words)

	Equivalence Relations
		They are reflexive, transitive and symmetric relations such that if it is required that for any context two systems behave in the same way, then these are congruences.
		The basic idea of a strong bisimulation relation is that two systems should be able to pass through equivalent states, such that one can simulate the others' behaviour at all times.
		Forming these relations is an iterative process, starting with the two systems initial states, and for each transition that each system can make, relating the resulting state to another state in the other system.
	www.cs.bris.ac.uk /~edwards/prep2001/html/node9.html (534 words)

	The Math Forum - Math Library - Calculus (SV)
		A WebQuest for Jeanne Winters' calculus students at Princeton Community High School, addressing the concepts of integration, elliptical curves, cylinders and the mathematical forces of gravity and lift.
		Interactive technology-based modules for the engineering calculus sequence which emphasize geometric concepts of calculus while examining applications of mathematics to the physical and life sciences.
		According to some Calculus textbooks, 0^0 is an "indeterminate form"; in some cases we think about it as having one value, and in other cases as having another...
	mathforum.org /library/topics/svcalc (2641 words)

	433-441 System Modelling and Analysis
		Topics covered include: Objectives of system modeling; the form and content of different modeling theories; modeling systems using logic and set theory, theories for modeling and analyzing concurrent and interacting systems including automata, Petri-nets and process algebras; developing and understanding models of a system.
		The essence of this subject is to learn how to build models of digital systems, the methods and notations available for building models, determining good models from bad and in understanding their analysis.
		This subject aims to explore the issues surrounding the use of mathematical theories for modeling systems with a specific focus on Automata, the Calculus of Communicating Systems, Petri Nets and Z amongst other formalisms.
	www.cs.mu.oz.au /441 (1086 words)

	The Math Forum - Math Library - Calculus (MV) (Site not responding. Last check: 2007-11-03)
		A calculus textbook in postscript and PDF formats, with Java applets for: Sequences, limits, and difference equations (area of a circle; tangent line for a parabola; inhibited population growth); Functions and their properties (square wave approximation;...more>>
		A computer-based course about calculus, differential equations, and matrix theory, which the instructor can use as soon as the computers are unloaded at the classroom door.
		Maple worksheets for courses in single- and multi-variable calculus, linear algebra, abstract algebra, and cryptography and coding theory may be downloaded here.
	mathforum.org /library/topics/mvcalc (2219 words)

	ANALYZE - bisimulation based verification
		This is a tool which helps to fill the tool need in the domain of formal asynchronous circuit and system verification.
		Although asynchronous systems can be based on formal handshake semantics, "equality" between behavioral descriptions and implementations has been difficult to formally define.
		Bisimulation, and a property I define as "conformance" can be combined to formally prove satisfaction between arbitrary hierarchies of asynchronous components and systems and their specifications.
	kdstevens.com /~stevens/analyze-page.html (532 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Series: Logic Seminar Date: Tuesday, April 7, 1998 Time: 2:30 PM Place: 308 Boucke Building Title: Communication and Choice in Mobile Networks Speaker: Catuscia Palamidessi (Penn State CSE) Abstract: The Pi-Calculus is an extension of Milner's CCS (Calculus for Communicating Systems) with mechanisms for Mobility, i.e.
		Several variants of this calculus have been developed for specific applications, and, surprisingly enough, most of them have been proved equivalent from the point of view of expressiveness.
		It has been shown that both synchronous communication and input-guarded choice can be simulated in the Asynchronous Pi-Calculus, and an implementation of it has been developed (by Benjamin Pierce, at Indiana University).
	www.math.psu.edu /simpson/logic/seminar/980407.txt (255 words)

	Introduction to a Calculus of Communicating Systems (Site not responding. Last check: 2007-11-03)
		The bulk of the material presented was drawn from a set of lecture notes written by Milner in the autumn of 1986, these being a development and refinement of their author's monograph ``A Calculus of Communicating Systems'' published by Springer-Verlag in 1980.
		Milner's notes provide both a description of the calculus and a full account of its mathematical foundations.
		Their comprehensive nature, however, does not help to make them an ideal introduction to the calculus for a reader not primarily interested in the underlying mathematics.
	www.lfcs.inf.ed.ac.uk /reports/86/ECS-LFCS-86-22/index.html (138 words)

	Reference.com/Encyclopedia/Pi-calculus
		-calculus is a process calculus originally developed by Robin Milner, Joachim Parrow and David Walker as a continuation of the body of work on the process calculus CCS (Calculus of Communicating Systems).
		The simplicity of the calculus is due to the fact that names play a dual role as communication channels and variables.
		As of July 2006, there is discussion in the community as to how useful this will be.
	www.reference.com /browse/wiki/Pi-calculus (1727 words)

	Foundations of Concurrent Programming Languages and Systems
		CCS (a Calculus for Communicating Systems) - I
		Communicating and mobile systems : the π-calculus - II - Ch.
		Communicating and mobile systems : the π-calculus - III
	yangtze.cs.uiuc.edu /cs524/index_2001s_.html (447 words)

	Join Java
		Communicating Sequential Processes (CSP), Calculus of Communicating Systems (CCS) and Pi have higher-level synchronization behaviours defined implicitly through the composition of events at the interfaces of concurrent processes.
		Join calculus, on the other hand has explicit synchronization based on a localized conjunction of events defined as reduction rules.
		The synchronization expressions associated with monitors (wait and notify) which are normally located in the body of methods can be replaced by Join Java expressions (the Join patterns) which form part of the method signature.
	joinjava.unisa.edu.au (428 words)

	CIS 700: Pi Calculus and Foundations of Concurrent Systems (Site not responding. Last check: 2007-11-03)
		However, despite the widespread use of both multithreaded and distributed programs, reasoning about the synchronization and interprocess communication behavior of concurrent systems is challenging.
		-calculus is a minimal programming language designed for studying key features of concurrent systems, including synchronization and message passing.
		As time permits, the latter part of the course will explore type systems for process calculi and the current research on designing programming languages that make it easier to reason about process behavior, for instance to rule out dead lock.
	www.cis.upenn.edu /~stevez/CIS700-04.html (148 words)

	Rance Cleaveland's Publications: 2002 (Site not responding. Last check: 2007-11-03)
		Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation--free linear--time mu--calculus (LTm).
		From a technical point of view, the new calculus is distinguished by the inclusion of (i) both minimal and maximal fixed--point operators and (ii) an unimplementability predicate on process terms which tags inconsistent specifications.
		The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.
	www.cs.umd.edu /~rance/publications/2002.html (491 words)

	Toinette Rorie, M.S. Student, Dept. of Computer Science, North Carolina A&T State University (Site not responding. Last check: 2007-11-03)
		-calculus, a calculus for communicating systems where one can express processes that have changing structure, can be used to model aspects of multi-agent systems.
		Process algebras are term algebras that can be used to describe communicating concurrent processes, to specify concurrent systems, and to refine specifications down to the level of designs.
		The immediate significance of this work is that it shows how multi-agent systems may be formally specified and how existing multi-agent systems may be formally modeled and analyzed.
	www.ncat.edu /~agents/abstracts/Toinette.html (456 words)

	Proposal Report
		Believing that the common semantic framework of mathematical functions for sequential programming is not enough to explain concurrency,Robert Milner developed a semantic theory of processes called Calculus of Communicating Systems.
		It provides simple and elegant proof techniques for showing that a process implementation meets its specifications.So it is actually very valuable for practical purposes as well as laying a theoretical basis for concurrent and communicating systems.
		But since it can prove that a system meets its specifications, it is worth to use to verify for safety critical systems, like air-ground data link protocols.
	www.ceng.metu.edu.tr /~irem/proposal.html (519 words)

	Communicating Automata and Pi Calculus (Site not responding. Last check: 2007-11-03)
		Examples of synchronised interaction; concurrent combination of automata; observation equivalence of automata; calculus of communicating systems (CCS) and its algebraic properties; examples of non-trivial concurrent systems and their analysis.
		Examples of systems with dynamic reconfiguration, and their presentation; formal syntax of the pi calculus; rationale for this new basic model.
		Sorts, the type discipline of pi calculus; theoretical soundness of sorting; sorts in applications; functional programming as an application; the higher-order pi calculus.
	www.cl.cam.ac.uk /DeptInfo/CST97/node64.html (175 words)

	Information and Computation Bibliography (Site not responding. Last check: 2007-11-03)
		We present the pi-calculus, a calculus of communicating systems in which one can naturally express processes which have changing structure.
		A calculus for cryptographic protocols: The spi calculus.
		The lazy lambda calculus in a concurrency scenario.
	theory.lcs.mit.edu /~iandc/References/milnerpw1992:1.html (933 words)

	epowiki: Process Calculus (Site not responding. Last check: 2007-11-03)
		A formal language used to specify the actions of processes and their sequential and concurrent composition.
		A process calculus has a formal semantics which is useful in attempts to prove certain properties about a software design, such as freedom from DeadLock or LiveLock, or that resources are fairly shared between concurrent processes.
		Calculus Of Communicating Systems (Robin Milner, Turing Award 1991)
	www.possibility.com /epowiki/Wiki.jsp?page=ProcessCalculus (71 words)

	Robin Milner (Site not responding. Last check: 2007-11-03)
		From 1971 to 1980, at Stanford and Edinburgh, he worked on computer-assisted reasoning; with colleagues he developed LCF (Logic for Computable Functions), a system for machine-assisted formal reasoning.
		His main work has been in the theory of concurrent computation.
		These calculi are part of a continuing quest for a theory which unites computing and communication.
	www.cse.ogi.edu /tphols2000/milner.htm (236 words)

	Lecture Notes in Real-Time Systems (Site not responding. Last check: 2007-11-03)
		Lecture 10: CCS (Calculus of Communicating Systems) & RTS I
		Lecture 11: CCS (Calculus of Communicating Systems) & RTS II Lecture 12: CCS (Calculus of Communicating Systems) & RTS III
		Lecture 13: CCS (Calculus of Communicating Systems) & RTS IV Lecture 14: CSP (Communicating Sequential Processes) & RTS I
	www-users.aston.ac.uk /~yans/RTS/RTS.html (150 words)

	Process Algebra (Site not responding. Last check: 2007-11-03)
		The department of mathematics which investigates the relations and properties of numbers by means of general symbols; and, in a more abstract sense, a calculus of symbols combining according to certain defined laws.
		An algebraic approach to the study of concurrent processes.
		The former use still occurs in [BW90] and [He88] for instance, but the latter, to which I also subscribe, is more widespread now.
	theory.stanford.edu /~rvg/process.html (352 words)

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