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Topic: Pi-Calculus

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Calculus (disambiguation) - Wikipedia, the free encyclopedia Tuple calculus, a calculus for the relational data model, inspired the SQL language. Precalculus is a family of mathematical topics that prepare students to begin to study differential and integral calculus. Calculus (medicine) is a stone formed in the body such as a gall stone or kidney stone. en.wikipedia.org /wiki/Calculus_(disambiguation)   (313 words)

Pi-calculus - Wikipedia, the free encyclopedia This can be seen by the fact the bisimulation equivalence becomes decidable for the recursion-free calculus and even for the finite-control π-calculus where the number of parallel components in any process is bounded by a constant (Mads Dam: On the Decidability of Process Equivalences for the pi-Calculus. The π-calculus is in the family of process calculi that have been used to model concurrent programming languages just as the λ-calculus has been used to model sequential programming languages. The sets of free and bound names of a process in π–calculus are defined inductively as follows. en.wikipedia.org /wiki/Pi-calculus   (1769 words)

Nominal Calculi for Security and Mobility The spi calculus [1] is a version of the pi calculus that allows communication on a cryptographic channel to be modelled as communication on a public channel of a term that represents a ciphertext. The pi calculus was published as a ``A Calculus of Mobile Processes'' [12] because, unlike almost all previous process calculi, its mobile restrictions can model the passage of knowledge of a communications channel from one process to another. The pi calculus of Milner, Parrow and Walker [ 12] is a nominal calculus in which computations consist of collections of parallel processes equipped with synchronous communication channels. www.cs.nps.navy.mil /research/languages/statements/gordon.html   (2167 words)

bibliography.bib The prototypical calculus %% in the first-­order paradigm is the pi-­calculus. The expressive %% power of the calculus is demonstrated by giving a straight­forward encoding %% of the strong lazy lambda—­calculus, which admits reduction under %% lamda—abstraction. We provide a detailed presentation of some of %% the theory of the calculus developed to date, and in particular we establish %% most of the results stated in the companion paper. www.cs.mu.oz.au /~rgm/bibliography.bib   (1340 words)

Business Process eXcellence (BPX): Pi Calculus Pi Calculus is not a logic, rather, a unified representation for things we previously thought were different. Pi Calculus is not a variant of the Lambda Calculus. However, Pi Calculus is the best unification of process we have, it won the Nobel Prize for computing, the ACM Turing Award, and so, until someone comes up with something better, it’s a good basis on which to build BPM tools. delphigroup.blogs.com /bpx2004/2004/10/pi_calculus.html   (958 words)

A page about process calculus A lecture by the founding father of the pi calculus, though he would immediately urge me to say that pi calculus, and concurrency theory in general, is a huge field to which many individuals have each made significant contributions. As Wischik says, pi calculus has come to dominate theoretical research into concurrency and distribution, but now its time has come to be used in practice. It goes without saying that the pi calculus and its predecessor, CCS, a general theory of concurrency, are very significant contributions to computer science. www.fairdene.com /picalculus   (677 words)

Manageability - Quick Take on the Pi Calculus Pi calculus is a fairly recent formulation of computation that strives to take into account mobile processes. So if you could extrapolate that the lambda calculus modeled recursive computation, the relational calculus modeled data and now you have the Pi calculus models process. From our discussion I hear that pi gives me: 1) automatic deadlock detection, 2) a formal composition model that let me describe that how messages are interchaged 3) automatic verification (simulation) that something is going to work. www.manageability.org /blog/stuff/quick-take-on-pi-calculus/view   (698 words)

Selected Bibliography on Mobile Processes Pi-calculus is a calculus of names and their manipulation, and as such the basic understanding of the mathematics of names would be important for its understanding. Its core calculus differs from the usual presentation of pi-calculi in that recursion and name passing are combined to form a single operation. Another interesting topic on this calculus is the existence of combinatory representation, just as SKI combinators for lambda-calculus. www.di.fc.ul.pt /~vv/mobilebib.html   (5458 words)

Calculus - A Great Resource of Information Calculus Tutorials and Problems Free tutorials that may be used to explore a new topic or as a... Calculus is a branch of mathematics, developed from algebra and geometry, involving two major complementary ideas: The first, called differential calculus is a theory about rates of change, and...     This is a textbook for a course in multivariable calculus. www.aboutcalculus.com   (1390 words)

confer2-paris.txt We provide embeddings of the $pi$-calculus, the $\pi_I$-calculus and the fusion calculus in the $\pi_F$-calculus, and show the connection between a bisimulation congruence for the $\pi$-calculus and the bisimulation congruence arising from its translation in the $\pi_F$-calculus. Then we give a representation of the spi calculus in the Edimburg Logical Framework. The calculus naturally provides an efficient notion of reduction (with a high degree of sharing), which can easily be implemented. www.cl.cam.ac.uk /users/pes20/confer2-paris.txt   (1075 words)

pi working group at ACI vicanne Gene regulation in the pi calculus: simulating cooperativity at the lambda switch (C. Kuttler and J. Niehren). The pi calculus as an abstraction for biomolecular systems by A.Regev and E. Shapiro (2004). The variant of pi presented is based on Priami's stochastic pi calculus. www.lifl.fr /~kuttler/misc/vicanne-nice2005.html   (323 words)

INI Programme SEM workshop The talk is thus an invitation to the hacking in pi-calculus and its descendants (you can even hack with its combinators!), by which we may arrive at languages constructs with higher-level abstraction, and which, by the way, itself is a fun to do. Instead, according to previous results only pairs of pi agents could be unfolded and tested for bisimilarity, and no minimization of a single agent was possible. The $\delta$-calculus is a relational calculus with procedural abstraction and application. www.newton.cam.ac.uk /programmes/SEM/hlcl.html   (1272 words)

Robin Milner 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. It is an aim of his there to find a foundation for concurrency as basic as the lambda calculus is for sequential computation. www.fairdene.com /picalculus/robinmilner.html   (2214 words)

Philip Wadler: Largely lambda, with a slice of pi One way to embed pi calculus in lambda calculus is to augment the lambda calculus with one constant for each construct of the pi calculus, modeling binding with higher-order functions in the way first suggested by Church. Lambda calculus remains a source of inspiration for work on concurrent calculi, and so the first part of the talk summarised some recent developments in lambda calculus. The second part of the talk reversed the usual idea of embedding lambda calculus within pi calculus, and compared two sets of primitives for embedding pi calculus within lambda calculus. www.ps.uni-sb.de /~mmueller/events/wadler.html   (889 words)

Pi Thanks to Newton, Leibniz, and the other calculus greats, we know that the antiderivative, without limits of integration, of 1/(1+x^2) is arctan(x) + a constant, because the derivative of any constant by itself is 0. Of course, only an infinite number of terms would add up to pi exactly, but pi is an infinite, transcendental number and can only be approached through approximation for this reason. In calculus, the angle x is always measured in radians. members.aol.com /purseweb/calc.html   (901 words)

Project Default Page To compose programs, a convient notation similar to the actual syntax of the pi calculus is used, and an intuitive interface allows access to the functions of the tool. A previous implementation of the lambda calculus had been developed in Prolog, and during the course of the development Prolog proved itself to be the ideal language for designing such a tool. This test clearly demonstrates the utility of the PI tool. www.cs.ucd.ie /ideasDay/projects00/rhayes   (341 words)

Action Structures and the Pi-Calculus Action structures were later introduced as a family of calculi (including the Pi-Calculus and many familiar models of computation such as the Lambda Calculus and Petri nets), with the aim of allowing such models to be compared and combined, and to develop their common theory. The Pi-Calculus is a fundamental calculus for interactive computing defined in about 1990. Finally, we have identified and partially solved a hard semantic problem, to define a notion of behavioural equivalence with tractable properties for a wide class of action calculi, which agrees with any specialized theory which exists for each individual calculus. www.cl.cam.ac.uk /users/pes20/grk38403.html   (592 words)

Recovering resources in the pi-calculus Lambda the Ultimate We show that the typed region calculus of Tofte and Talpin can be encoded in a typed pi-calculus equipped with name groups and a novel effect analysis. I hadn't considered a link between region allocation and pi calculus before. In the region calculus, each boxed value has a statically determined region in which it is stored. lambda-the-ultimate.org /node/view/615   (502 words)

LearnThis.Info Encyclopedia articles beginning with 'Pi' P > Pi Listed below are all articles that begin with Pi. encyclopedia.learnthis.info /p/pi/index.html   (60 words)

Pi Calculus for SOA 1.3.0 released - tool for choreography The global calculus is similar to WS-CDL and the main point of the paper is that processes modeled with the global calculus (WS-CDL) can all be translated to the pi-calculus. In the paper linked to above two formal calculi are described: a 'global' calculus that models business processes from a global perspective and the pi-calculus that models the same processes as a set of local endpoint behaviors. Posted by: Steve Ross-Talbot on November 24, 2005 @ 03:27 PM Pi4 Technologies is pleased to announce release 1.3.0 of it's WS-CDL eclipse-based open source tool suite called Pi Calculus for SOA. www.theserverside.com /news/thread.tss?thread_id=37760   (3107 words)

pict.html This gives pi-calclus the partial flavor of a "calculus of mobile processes," as it is sometimes called. Pi-calculus is a form of process calculus, as considered in earlier lectures. Process calculus, on the other hand, is generally presented as a synchronous system. theory.stanford.edu /people/jcm/cs358-96/pict.html   (1904 words)

Pi-calculus Davide Sangiorgi and David Walker: The Pi-calculus: A Theory of Mobile Processes'', Cambridge University Press, ISBN 0521781779 It uses material from the Wiktionary page "Calculus". From Latin calculus, pebble (used for counting), diminuitive from calx, limestone, + diminuitive suffix -ulus www.serebella.com /encyclopedia/article-Pi-calculus.html   (384 words)

Pi Day Resources Pi Day Activities, part II Below are some pi links arranged by category. 300th Anniversary of Pi he sixteenth letter of the Greek alphabet, p, was first used for the familiar value 3.1415 in the publication, “Synopsis Palmariorium Mathesios”, authored by William Jones in 1706. This book is a collection of articles following pi from the early days of mathematics to the present. www.mobot.org /education/megsl/pi.html   (454 words)

Two papers on the pi-calculus. While our work so far, some of which we announce here, is just the beginning, we hope it will open new ways to use this calculus for the study of types of programming languages and computation. The typed calculus allows direct interpretation of both call-by-name and call-by-value sequential functions. The precision of the representation is demonstrated by way of a fully abstract encoding of PCF. www.seas.upenn.edu /~sweirich/types/archive/1999-2003/msg00733.html   (412 words)

The pi-Calculus in Direct Style Lambda the Ultimate This calculus is both an extension of Abadi & Cardelli's &-calculus [AC96] and the Milner's pi-calculus [Mil93]. We develop a calculus which is a "direct" descendant of the blue calculus of Boudol [Bou97]. This transform shows that the latter can be seen as a "target language", while our calculus provide a very expressive and promising notation for higher-order object-oriented concurrent programming languages. lambda-the-ultimate.org /node/view/506   (503 words)

CFP: JLAP special issue on pi-calculus In pi-calculus, the simple idea is to allow processes to exchange specific values -channel names themselves- and thereby to dynamically change their interconnection structures: processes become mobile. The pi-calculus, originally introduced by Robin Milner, Joachim Parrow, and David Walker back in 1989 arose as a generalization of the algebraic process calculus CCS. The Journal of Logic and Algebraic Programming complements Elsevier's Science of Computer Programming and Theoretical Computer Science by its focus on the foundations of logical, algebraic and categorical methods for programming. www.seas.upenn.edu /~sweirich/types/archive/1999-2003/msg00590.html   (320 words)

pi-calc.bib % $Id: pi-calc.bib,v 1.1.1.1 2002/03/26 16:48:03 cclifton Exp $ %Subject: pi calculus refs? To address this problem, we propose the development of an object calculus, borrowing heavily from relevant work in the area of process calculi. Furthermore, the delicate relationship between object-oriented features supporting reuse and operational features concerning interaction and state change is poorly understood in a concurrent setting. www.cs.iastate.edu /~leavens/include/pi-calc.bib   (279 words)

pifirst.html So yes, JSR121 is clearly pi-derived in the sense that it has at least some direct mappings to pi calculus and the potential for the benefit that stems from them. JSR-121 associations with pi calculus and pi calculus relevance to mobile agent systems will stimulate interest in the isolation APIs. The Pi Calculus, Mobility and JSR-121: First Thoughts bitser.net /isolate-interest/papers/pifirst.html   (677 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. Its theory has two important ingredients: the concept of behavioural (or observational) equivalence, and the use of a new theory of types to classify patterns of interactive behaviour. One can also describe networks which reconfigure themselves. www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521658691   (224 words)

The pi-calculus Two such calculi, the stochastic pi-calculus and the ambient calculus are particularly important for our needs. A simple description of the syntax and semantics of the pi calculus can be found in our Luca Cardelli, facilitates the specification of process location and movement through domains, and can be used for the representation of various aspects of molecular localization and compartmentalization. www.wisdom.weizmann.ac.il /~aviv/pi.htm   (264 words)

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