## A brief history of process algebra (2004)

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Venue: | Theor. Comput. Sci |

Citations: | 57 - 1 self |

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@TECHREPORT{Baeten04abrief,

author = {J. C. M. Baeten},

title = {A brief history of process algebra},

institution = {Theor. Comput. Sci},

year = {2004}

}

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### Abstract

Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.

### Citations

3400 | Communicating Sequential Processes
- Hoare
- 1985
(Show Context)
Citation Context ...process can perform. Later on, it was found that this model was lacking, for instance because deadlock behaviour is not preserved. For this reason, a new model based on failure pairs was presented in =-=[29]-=- for the language that was then called TCSP (Theoretical CSP). Later,s8 J.C.M. Baeten TCSP was called CSP again. Some time later it was established that the failure model is the least discriminating m... |

3204 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...t was realized just after the appearance of [72] is the formulation of bisimulation by David Park [83]. This became a central notion in process theory subsequently. The book [72] was later updated in =-=[75]-=-. A related development is the birth of structural operational semantics in [86]. More can be read about this in the recent history paper [87]. 3.3 CSP A very important contributor to the development ... |

1361 | An axiomatic basis for computer programming
- Hoare
- 1969
(Show Context)
Citation Context ...hods proving programs correct. Central notions are program assertions, proof triples consisting of precondition, program statement and postcondition, and invariants. Pioneers are Floyd [38] and Hoare =-=[53]-=-. Then, the question was raised how to give semantics to programs containing a parallel operator. It was found that this is difficult using the methods of denotational, operational or axiomatic semant... |

1329 |
A calculus of communicating systems
- Milner
- 1980
(Show Context)
Citation Context ... are | for parallel composition, restriction and relabeling. The symbol � is now reserved for restricted parallel composition. Static laws are stated for these operators. The following two papers are =-=[69, 70]-=-, putting in place most of CCS as we know it. The dynamic operators prefixing and alternative composition are added and provided with laws. Synchronization trees are used as a model. The prefix τ occu... |

1286 | A structural approach to operational semantics
- Plotkin
- 1981
(Show Context)
Citation Context ...ion by David Park [83]. This became a central notion in process theory subsequently. The book [72] was later updated in [75]. A related development is the birth of structural operational semantics in =-=[86]-=-. More can be read about this in the recent history paper [87]. 3.3 CSP A very important contributor to the development of process algebra is Tony Hoare. C.A.R. Hoare, born in 1934, published the infl... |

1204 |
The temporal logic of programs
- Pnueli
- 1977
(Show Context)
Citation Context ... activity world wide. We already mentioned research on Petri nets, that is an active area [85]. Another partial order process theory is given in [63]. Research on temporal logic has started, see e.g. =-=[88]-=-. Some other process theories can be mentioned. We already remarked that Hoare investigated trace theory. More work was done in this direction, e.g. by Rem [90]. There is also the invariants calculus ... |

995 | A calculus of mobile processes
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ...rch on networks of processes where processes are mobile and configuration of communication links is dynamic has been dominated by the π-calculus. An early reference is [36], the standard reference is =-=[79]-=- and the textbook is [77]. The associated tool is the Mobility Workbench, see [94]. Also in this domain, it is important to gain more experience with protocol verification. On the theory side, there a... |

809 | Mobile Ambients
- Cardelli, Gordon
- 1998
(Show Context)
Citation Context ...erent equivalences that have been defined, and it is not clear which is the ‘right’ one to use. More recently, other calculi concerning mobility have been developed, notably the ambient calculus, see =-=[31]-=-. As to unifying frameworks for different mobile calculi, Milner investigates action calculus [76] and bigraphs [78]. 4.7 Probabilities and Stochastics Process algebras extended with probabilistic or ... |

655 |
Concurrency and automata on infinite sequences
- Park
- 1981
(Show Context)
Citation Context ...e laws as primary, and investigating the range of models that they have. An important contribution that was realized just after the appearance of [72] is the formulation of bisimulation by David Park =-=[83]-=-. This became a central notion in process theory subsequently. The book [72] was later updated in [75]. A related development is the birth of structural operational semantics in [86]. More can be read... |

596 | The algorithmic analysis of hybrid systems
- Alur, Courcoubetis, et al.
- 1995
(Show Context)
Citation Context ... dynamic control theory are very important. Here, process algebra research is just at the beginning. The attempts [24, 32] are worth mentioning. In process theory, work centres around hybrid automata =-=[4]-=- and hybrid I/O automata [60]. A tool is HyTech, see [51]. A connection with process algebra can be found in [95]. 5 Conclusion In this note, a brief history is sketched of process algebra. The early ... |

596 | A Compositional Approach to Performance Modeling
- Hillston
- 1996
(Show Context)
Citation Context ... algebras extended with probabilistic or stochastic information have generated a lot of research in recent years. An early reference is [47]. In the CSP tradition, there is [59], in the CCS tradition =-=[52]-=-, in the ACP tradition [12]. There is the process algebra TIPP with associated tool, see e.g. [43], and EMPA, see e.g. [26]. Recently, the insight that both (unquantified) alternative composition and ... |

587 |
Communicating and Mobile Systems: the π-Calculus
- Milner
- 1999
(Show Context)
Citation Context ...ses where processes are mobile and configuration of communication links is dynamic has been dominated by the π-calculus. An early reference is [36], the standard reference is [79] and the textbook is =-=[77]-=-. The associated tool is the Mobility Workbench, see [94]. Also in this domain, it is important to gain more experience with protocol verification. On the theory side, there are a number of different ... |

563 |
Assigning meanings to programs
- Floyd
- 1967
(Show Context)
Citation Context ...ut on proof methods proving programs correct. Central notions are program assertions, proof triples consisting of precondition, program statement and postcondition, and invariants. Pioneers are Floyd =-=[38]-=- and Hoare [53]. Then, the question was raised how to give semantics to programs containing a parallel operator. It was found that this is difficult using the methods of denotational, operational or a... |

491 | UPPAAL in a nutshell
- Larsen, Pettersson, et al.
- 1997
(Show Context)
Citation Context ... experience with verification of functional behaviour and timing behaviour is certainly needed. Tooling has been developed for processes with timing mostly in terms of timed automata, see e.g. UPPAAL =-=[57]-=- or KRONOS [97]. Equational reasoning is investigated for µCRL with timing [93]. 4.6 Mobility Research on networks of processes where processes are mobile and configuration of communication links is d... |

413 |
Guarded commands, nondeterminacy and formal derivation of programs
- Dijkstra
- 1975
(Show Context)
Citation Context ...unication, thus realizing the second paragdigm shift. The language CSP (Communicating Sequential Processes) described in [54] has synchronous communication and is a guarded command language (based on =-=[35]-=-). No model or semantics is provided. This paper inspired Milner to treat message passing in CCS in the same way. A model for CSP was elaborated in [55]. This is a model based on trace theory, i.e. on... |

393 |
Algebraic Theory of Processes
- Hennessy
- 1988
(Show Context)
Citation Context ...ommunication is combined with restriction. 3.6 Further Remarks In later years, other process algebras were developed. We can mention SCCS [73], CIRCAL [65], MEIJE [7], the process algebra of Hennessy =-=[48]-=-. We see that over the years many process algebras have been developed, each making its own set of choices in the different possibilities. The reader may wonder whether this is something to be lamente... |

360 | Process algebra for synchronous communication
- Bergstra, Klop
- 1984
(Show Context)
Citation Context ... given by a sequence of approximations by finite terms), and in this model, it is established that all recursive equations have a solution. In adapted form, this paper was later published as [23]. In =-=[22]-=-, this process algebra PA was extended with communication to yield the theory ACP (Algebra of Communicating Processes). The book [15] gives an overview of ACP. Comparing the three most well-known proc... |

350 |
Kommunication mit Automaten
- Petri
- 1962
(Show Context)
Citation Context ... back to the early seventies of the twentieth century. At that point, the only part of concurrency theory that existed is the theory of Petri nets, conceived by Petri starting from his thesis in 1962 =-=[84]-=-. In 1970, we can distinguish three main styles of formal reasoning about computer programs, focusing on giving semantics (meaning) to programming languages. 1. Operational semantics. A computer progr... |

311 |
Calculi for Synchrony and Asynchrony
- Milner
- 1983
(Show Context)
Citation Context ... in CCS, communication is combined with abstraction, in CSP, communication is combined with restriction. 3.6 Further Remarks In later years, other process algebras were developed. We can mention SCCS =-=[73]-=-, CIRCAL [65], MEIJE [7], the process algebra of Hennessy [48]. We see that over the years many process algebras have been developed, each making its own set of choices in the different possibilities.... |

289 | The linear time - branching time spectrum
- Glabbeek
- 1990
(Show Context)
Citation Context ...on was proposed in [42] with certain advantages [40]. In between bisimulation and trace equivalence there is a wholes10 J.C.M. Baeten lattice of other equivalences, see the overview in [41]. See also =-=[39]-=-. For process algebra based on partial order semantics, see [27]. There is a wealth of results concerning process algebra extended with some form of recursion, see e.g. the complete axiomatization of ... |

255 | Branching Time and Abstraction in Bisimulation Semantics
- Glabbeek, Weijland
- 1996
(Show Context)
Citation Context ...tion by Park [83]. Strong bisimulation and weak bisimulation became the central notion of equivalence in process theory. As an alternative to weak bisimulation, branching bisimulation was proposed in =-=[42]-=- with certain advantages [40]. In between bisimulation and trace equivalence there is a wholes10 J.C.M. Baeten lattice of other equivalences, see the overview in [41]. See also [39]. For process algeb... |

210 |
Kronos: A Verification Tool for Real-time Systems
- Yovine
- 1997
(Show Context)
Citation Context ...h verification of functional behaviour and timing behaviour is certainly needed. Tooling has been developed for processes with timing mostly in terms of timed automata, see e.g. UPPAAL [57] or KRONOS =-=[97]-=-. Equational reasoning is investigated for µCRL with timing [93]. 4.6 Mobility Research on networks of processes where processes are mobile and configuration of communication links is dynamic has been... |

202 | A Basis for a Mathematical Theory of Computation
- McCarthy
- 1963
(Show Context)
Citation Context ...eled as an execution of an abstract machine. A state of such a machine is a valuation of variables, a transition between states is an elementary program instruction. Pioneer of this field is McCarthy =-=[64]-=-. 2. Denotational semantics. More abstract than operational semantics, computer programs are usually modeled by a function transforming input into output. Most well-known are Scott and Strachey [92]. ... |

172 |
A temporal calculus of communicating systems
- Moller, Tofts
- 1990
(Show Context)
Citation Context ...h a quantitative notion of time started with the work of Reed and Roscoe in the CSP context, see [89]. A textbook in this tradition is [91]. There are many variants of CCS with timing, see e.g. [96], =-=[81]-=-. In the ACP tradition, work starts with [10]. An integrated theory, involving both discrete and dense time, both relative and absolute time, is presented in the book [13]. Also the theory ATP can be ... |

156 | A timed model for communicating sequential processes
- Reed, Roscoe
- 1988
(Show Context)
Citation Context ... data parameters.s4.5 Time Brief History of Process Algebra 11 Research on process algebra extended with a quantitative notion of time started with the work of Reed and Roscoe in the CSP context, see =-=[89]-=-. A textbook in this tradition is [91]. There are many variants of CCS with timing, see e.g. [96], [81]. In the ACP tradition, work starts with [10]. An integrated theory, involving both discrete and ... |

155 | Real time process algebra
- Baeten, Bergstra
- 1991
(Show Context)
Citation Context ...the work of Reed and Roscoe in the CSP context, see [89]. A textbook in this tradition is [91]. There are many variants of CCS with timing, see e.g. [96], [81]. In the ACP tradition, work starts with =-=[10]-=-. An integrated theory, involving both discrete and dense time, both relative and absolute time, is presented in the book [13]. Also the theory ATP can be mentioned, see [82]. There are many formulati... |

150 | Elements of interaction
- Milner
- 1993
(Show Context)
Citation Context ...re recently, other calculi concerning mobility have been developed, notably the ambient calculus, see [31]. As to unifying frameworks for different mobile calculi, Milner investigates action calculus =-=[76]-=- and bigraphs [78]. 4.7 Probabilities and Stochastics Process algebras extended with probabilistic or stochastic information have generated a lot of research in recent years. An early reference is [47... |

147 |
Time and probability in formal design of distributed systems
- Hansson
- 1994
(Show Context)
Citation Context ...76] and bigraphs [78]. 4.7 Probabilities and Stochastics Process algebras extended with probabilistic or stochastic information have generated a lot of research in recent years. An early reference is =-=[47]-=-. In the CSP tradition, there is [59], in the CCS tradition [52], in the ACP tradition [12]. There is the process algebra TIPP with associated tool, see e.g. [43], and EMPA, see e.g. [26]. Recently, t... |

134 | Hybrid I/O automata
- Lynch, Segala, et al.
- 2003
(Show Context)
Citation Context ...very important. Here, process algebra research is just at the beginning. The attempts [24, 32] are worth mentioning. In process theory, work centres around hybrid automata [4] and hybrid I/O automata =-=[60]-=-. A tool is HyTech, see [51]. A connection with process algebra can be found in [95]. 5 Conclusion In this note, a brief history is sketched of process algebra. The early work centred around giving se... |

130 |
Toward a mathematical semantics for computer languages
- Scott, Strachey
- 1971
(Show Context)
Citation Context ...y [64]. 2. Denotational semantics. More abstract than operational semantics, computer programs are usually modeled by a function transforming input into output. Most well-known are Scott and Strachey =-=[92]-=-. 3. Axiomatic semantics. Here, emphasis is put on proof methods proving programs correct. Central notions are program assertions, proof triples consisting of precondition, program statement and postc... |

122 |
Concurrent program schemes and their interpretations
- Mazurkiewicz
- 1977
(Show Context)
Citation Context ...ticular process theory is a vibrant field with a lot of activity world wide. We already mentioned research on Petri nets, that is an active area [85]. Another partial order process theory is given in =-=[63]-=-. Research on temporal logic has started, see e.g. [88]. Some other process theories can be mentioned. We already remarked that Hoare investigated trace theory. More work was done in this direction, e... |

122 |
A complete inference system for a class of regular behaviours
- Milner
- 1984
(Show Context)
Citation Context ...on partial order semantics, see [27]. There is a wealth of results concerning process algebra extended with some form of recursion, see e.g. the complete axiomatization of regular processes by Milner =-=[74]-=- or the overview on decidability in [30]. Structural operational semantics (SOS) has become the dominant way of providing a model for a process algebra. It is standard practice to provide a new operat... |

122 |
Concurrent and Real-time Systems: The CSP Approach
- Schneider
- 2000
(Show Context)
Citation Context ...ry of Process Algebra 11 Research on process algebra extended with a quantitative notion of time started with the work of Reed and Roscoe in the CSP context, see [89]. A textbook in this tradition is =-=[91]-=-. There are many variants of CCS with timing, see e.g. [96], [81]. In the ACP tradition, work starts with [10]. An integrated theory, involving both discrete and dense time, both relative and absolute... |

121 | Structural operational semantics
- Aceto, Fokkink, et al.
- 1999
(Show Context)
Citation Context ...rd practice to provide a new operation with SOS rules, even before an equational characterization is attempted. There are many results based on the formats of these rules. An overview can be found in =-=[3]-=-. Finally, there is a whole range of expressiveness results, some examples can be found in [21]. As is also stated in [1], there are many nice results, but also many remaining open problems. 4.2 Tooli... |

110 | M.: Multiprocessor and distributed systems design: The integration of functional specification and performance analysis using stochastic process algebras
- Gotz, Herzog, et al.
- 1993
(Show Context)
Citation Context ...n recent years. An early reference is [47]. In the CSP tradition, there is [59], in the CCS tradition [52], in the ACP tradition [12]. There is the process algebra TIPP with associated tool, see e.g. =-=[43]-=-, and EMPA, see e.g. [26]. Recently, the insight that both (unquantified) alternative composition and probabilistic choice are needed for a useful theory has gained attention, see e.g. the work in [33... |

105 | The algebra of timed processes ATP: theory and application
- Nicollin, Sifakis, et al.
- 1994
(Show Context)
Citation Context ...adition, work starts with [10]. An integrated theory, involving both discrete and dense time, both relative and absolute time, is presented in the book [13]. Also the theory ATP can be mentioned, see =-=[82]-=-. There are many formulations, in these works and elsewhere, of bisimulation that takes into account timing information. Mostly, the passage of time is treated as the occurrence of an action: bisimila... |

101 | HyTech: the next generation
- Henzinger, Ho, et al.
- 1995
(Show Context)
Citation Context ...s algebra research is just at the beginning. The attempts [24, 32] are worth mentioning. In process theory, work centres around hybrid automata [4] and hybrid I/O automata [60]. A tool is HyTech, see =-=[51]-=-. A connection with process algebra can be found in [95]. 5 Conclusion In this note, a brief history is sketched of process algebra. The early work centred around giving semantics to programming langu... |

95 | R.: A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time
- Bernardo, Gorrieri
- 1998
(Show Context)
Citation Context ...reference is [47]. In the CSP tradition, there is [59], in the CCS tradition [52], in the ACP tradition [12]. There is the process algebra TIPP with associated tool, see e.g. [43], and EMPA, see e.g. =-=[26]-=-. Recently, the insight that both (unquantified) alternative composition and probabilistic choice are needed for a useful theory has gained attention, see e.g. the work in [33] or [5].s12 J.C.M. Baete... |

94 | The linear time – branching time spectrum I; the semantics of concrete, sequential processes
- Glabbeek
- 2001
(Show Context)
Citation Context ...hing bisimulation was proposed in [42] with certain advantages [40]. In between bisimulation and trace equivalence there is a wholes10 J.C.M. Baeten lattice of other equivalences, see the overview in =-=[41]-=-. See also [39]. For process algebra based on partial order semantics, see [27]. There is a wealth of results concerning process algebra extended with some form of recursion, see e.g. the complete axi... |

90 | Full abstraction for a simple parallel programming language
- HENNESSY, PLOTKIN
- 1979
(Show Context)
Citation Context ...ograms containing a parallel operator. It was found that this is difficult using the methods of denotational, operational or axiomatic semantics, although several attempts are made (for instance, see =-=[50]-=-). There are two paradigm shifts that need to made, before a theory of parallel programs in terms of a process algebra can be developed. First of all, the idea of a behaviour as an input/output functi... |

78 |
J.I.Zucker: Processes and the Denotational Semantics of Concurrency
- Bakker
- 1982
(Show Context)
Citation Context ...eory. More work was done in this direction, e.g. by Rem [90]. There is also the invariants calculus [6]. Another process theory that should be mentioned is the metric approach by De Bakker and Zucker =-=[16, 17]-=-. There is a notion of distance between processes: processes that do not differ in behaviour before the nth step have a distance of at most 2 −n . This turns the domain of processes into a metric spac... |

74 |
On observing nondeterminism and concurrency
- Hennessy, Milner
- 1980
(Show Context)
Citation Context ...gle observer of a communicating system, and the expansion law is stated. Sequential composition is not a basic operator, but a derived one, using communication, abstraction and restriction. The paper =-=[49]-=-, with Matthew Hennessy, formulates basic CCS, with observational equivalence and strong equivalence defined inductively. Also, so-called Hennessy-Milner logic is introduced, which provides a logical ... |

68 | Verification of infinite structures
- Burkart, Caucal, et al.
- 2001
(Show Context)
Citation Context ...ere is a wealth of results concerning process algebra extended with some form of recursion, see e.g. the complete axiomatization of regular processes by Milner [74] or the overview on decidability in =-=[30]-=-. Structural operational semantics (SOS) has become the dominant way of providing a model for a process algebra. It is standard practice to provide a new operation with SOS rules, even before an equat... |

66 |
Axiomatizing probabilistic processes: ACP with generative probabilities
- Baeten, Bergstra, et al.
- 1995
(Show Context)
Citation Context ...babilistic or stochastic information have generated a lot of research in recent years. An early reference is [47]. In the CSP tradition, there is [59], in the CCS tradition [52], in the ACP tradition =-=[12]-=-. There is the process algebra TIPP with associated tool, see e.g. [43], and EMPA, see e.g. [26]. Recently, the insight that both (unquantified) alternative composition and probabilistic choice are ne... |

64 | Structural Operational Semantics
- Plotkin
- 1981
(Show Context)
Citation Context ...s theory subsequently. The book [72] was later updated in [75]. A related development is the birth of structural operational semantics in [86]. More can be read about this in the recent history paper =-=[87]-=-. 3.3 CSP A very important contributor to the development of process algebra is Tony Hoare. C.A.R. Hoare, born in 1934, published the influential paper [54] as a technical report in 1976. The importan... |

63 |
2001): Bigraphical Reactive Systems
- Milner
(Show Context)
Citation Context ... calculi concerning mobility have been developed, notably the ambient calculus, see [31]. As to unifying frameworks for different mobile calculi, Milner investigates action calculus [76] and bigraphs =-=[78]-=-. 4.7 Probabilities and Stochastics Process algebras extended with probabilistic or stochastic information have generated a lot of research in recent years. An early reference is [47]. In the CSP trad... |

62 | Confluence for process verification
- Groote, Sellink
- 1996
(Show Context)
Citation Context ...n A measure of success of process algebra is the systems that have been successfully verified by means of techniques that come from process algebra. A good overview of the current state of affairs is =-=[46]-=-. Process algebra focuses on equational reasoning. Other successful techniques are model checking and theorem proving. Combination of these different approaches proves to be very promising. 4.4 Data P... |

61 |
Real-time behaviour of asynchronous agents
- Yi
- 1990
(Show Context)
Citation Context ...ed with a quantitative notion of time started with the work of Reed and Roscoe in the CSP context, see [89]. A textbook in this tradition is [91]. There are many variants of CCS with timing, see e.g. =-=[96]-=-, [81]. In the ACP tradition, work starts with [10]. An integrated theory, involving both discrete and dense time, both relative and absolute time, is presented in the book [13]. Also the theory ATP c... |

60 |
The algebra of recursively defined processes and the algebra of regular processes
- Bergstra, Klop
- 1984
(Show Context)
Citation Context ...ion is attempted. There are many results based on the formats of these rules. An overview can be found in [3]. Finally, there is a whole range of expressiveness results, some examples can be found in =-=[21]-=-. As is also stated in [1], there are many nice results, but also many remaining open problems. 4.2 Tooling Over the years, several software systems have been developed in order to facilitate the appl... |

58 |
Concepts of net theory
- Petri
- 1973
(Show Context)
Citation Context ...ess Theories Around 1980, concurrency theory and in particular process theory is a vibrant field with a lot of activity world wide. We already mentioned research on Petri nets, that is an active area =-=[85]-=-. Another partial order process theory is given in [63]. Research on temporal logic has started, see e.g. [88]. Some other process theories can be mentioned. We already remarked that Hoare investigate... |