## Process Algebra with Explicit Termination (2000)

Citations: | 1 - 1 self |

### BibTeX

@TECHREPORT{Baeten00processalgebra,

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

title = {Process Algebra with Explicit Termination},

institution = {},

year = {2000}

}

### OpenURL

### Abstract

In ACP-style process algebra, the interpretation of a constant atomic action combines action execution with termination. In a setting with timing, di#erent forms of termination can be distinguished: some time termination, current time slice termination, urgent termination, termination in a virtual state. In a setting with the silent action # , we also have silent termination. This leads to problems with the interpretation of atomic actions in timed theories that involve some form of the empty process or some form of the silent action. Reflection on these problems lead to a re-design of basic process algebra, where action execution and termination are separated. Instead of actions as constants, we have action prefix operators. Sequential composition remains a basic operator, and thus we have two basic constants for termination, # for unsuccessful termination (deadlock) and # for successful termination (skip). Standard BPA, PA, ACP become SRM specifications of the new approach. The new ...

### Citations

3743 | Communicating Sequential Processes
- Hoare
- 1985
(Show Context)
Citation Context ... problems lead to a re-design of basic process algebra, where action execution and termination are separated. Instead of actions as constants, we have action prefix operators as in CCS [18] or in CSP =-=[17]-=-. As in CSP, but di#erent from CCS, we have that sequential composition remains a basic operator. As a consequence, we have two basic constants for termination, # for unsuccessful termination (deadloc... |

3510 |
Communication and concurrency
- Milner
- 1989
(Show Context)
Citation Context ...ection on these problems lead to a re-design of basic process algebra, where action execution and termination are separated. Instead of actions as constants, we have action prefix operators as in CCS =-=[18]-=- or in CSP [17]. As in CSP, but di#erent from CCS, we have that sequential composition remains a basic operator. As a consequence, we have two basic constants for termination, # for unsuccessful termi... |

392 | Process algebra for synchronous communication
- Bergstra, Klop
- 1984
(Show Context)
Citation Context ...(skip). Standard BPA, PA, ACP become SRM specifications of the new approach. The new approach has definite advantages over the standard approach. 1 Introduction In ACP-style process algebra (see e.g. =-=[11, 8, 7]-=-), the interpretation of a constant atomic action combines action execution with termination. In a setting with timing, di#erent forms of termination can be distinguished: some time termination, curre... |

283 | Branching Time and Abstraction in Bisimulation Semantics
- Glabeek, Weijland
- 1996
(Show Context)
Citation Context ...can be called deadlock: without executing a visible action, a state will be reached where the process is stuck. As semantical treatment of the silent step we choose rooted branching bisimulation (see =-=[16]-=-) rather than Milner's original weak bisimulation (see e.g. [18]), as the former is closer to an action interpretation, and all axioms of IPA that hold for all actions also hold for # . In a setting w... |

225 | Process Algebra
- Baeten, Weijland
- 1990
(Show Context)
Citation Context ...(skip). Standard BPA, PA, ACP become SRM specifications of the new approach. The new approach has definite advantages over the standard approach. 1 Introduction In ACP-style process algebra (see e.g. =-=[11, 8, 7]-=-), the interpretation of a constant atomic action combines action execution with termination. In a setting with timing, di#erent forms of termination can be distinguished: some time termination, curre... |

164 | Real Time Process Algebra
- Baeten, Bergstra
- 1991
(Show Context)
Citation Context ...nd two phase process algebras (see [5]). Instead, we can make the point by considering one member of this family, viz. process algebra with discrete time in relative timing in two phase notation (see =-=[4]-=-). Also, it is su#cient to consider the theory without parallel composition. We have the following syntax in addition to signature elements of SPA: . current time slice action prefix a, where a # A. T... |

72 |
The algebra of recursively defined processes and the algebra of regular processes
- Bergstra, Klop
- 1984
(Show Context)
Citation Context ...R of SPA is obtained if we add constants #X|E# only for finite linear E. IR is the model of regular processes, it is equivalent to the model of finite transition systems modulo bisimulation, see e.g. =-=[10]-=-. Again we can establish that IR is really smaller than G, a process in the di#erence is the counter C defined by the following specification (p standing for plus, m for minus): C = T C T = pS S = m# ... |

53 |
Process algebra with iteration and nesting
- Bergstra, Bethke, et al.
- 1994
(Show Context)
Citation Context ...ounter as a solution, as the counter has infinitely many di#erent states. Thus, we see sequential composition does add expressive power. Finally, the term model IP of SPA* is even smaller than IR. In =-=[9]-=- it is shown that there are regular processes that cannot be defined just using iteration. Just having prefix iteration, the di#erence can be found even more simply, consider e.g. X = abX. In the mode... |

53 |
An operational semantics for CSP
- Plotkin
- 1983
(Show Context)
Citation Context ...it also follows the fact, that SPA is a conservative extension of MPA. Next, we provide a model for SPA on the basis of structured operational rules (so-called SOS rules) in the style of Plotkin (see =-=[19]-=-). The rules in Table 2 define the following relations on closed SPA-terms: binary relations . a # . (for a # A) and a unary relation #. Intuitively, they have the following meaning: . x a # x # means... |

30 | Process algebra with timing: Real time and discrete time
- Baeten, Middelburg
- 2001
(Show Context)
Citation Context ...vident, however, when we consider timing. It is not necessary to look at the whole framework of discrete and dense timed, absolute and relative timed, time-stamped and two phase process algebras (see =-=[5]-=-). Instead, we can make the point by considering one member of this family, viz. process algebra with discrete time in relative timing in two phase notation (see [4]). Also, it is su#cient to consider... |

17 |
Nonaxiomatisability of equivalences over finite state processes
- SEWELL
- 1997
(Show Context)
Citation Context ...add iteration as a binary operator on SPA, where process x # y can iterate the behaviour of x until exiting by doing y, then a complete finite axiomatization cannot be found. This was shown by Sewell =-=[20]-=-. On the other hand, there are extensions of action prefix iteration that still have finite axiomatizations, see e.g. [1, 15]. We can look at the combination of prefix iteration and renaming. Here, th... |

16 |
Discrete time process algebra with abstraction
- Baeten, Bergstra
(Show Context)
Citation Context ... we also have silent termination. This leads to problems with the interpretation of atomic actions in timed theories that involve some form of the empty process or some form of the silent action, see =-=[3, 6]-=-. Reflection on these problems lead to a re-design of basic process algebra, where action execution and termination are separated. Instead of actions as constants, we have action prefix operators as i... |

16 |
Discrete-Time Process Algebra
- Vereijken
- 1997
(Show Context)
Citation Context ... ### means that x cannot execute a 1 ## transition, i.e. x cannot pass to the next time slice. Thus, we have here an SOS definition with negative premises. It is well-defined, however, as is shown in =-=[21]-=-. Using the technique of saturation, it is possible to avoid the negative premises, see [6]. ax a # x # # #x 1 ## x x 1 ## x # , y 1 ## y # x + y 1 ## x # + y # x 1 ## x # , y 1 ### x + y 1 ## x # y 1... |

14 |
Top-down design and the algebra of communicating processes
- Bergstra, Tucker
- 1985
(Show Context)
Citation Context ...m in our theory. We do so, nevertheless, since it is such a basic result, that we will always assume that it holds for all processes. Its status is comparable to the axioms of standard concurrency of =-=[12]-=-. Since we have action prefixing as a separate operator, besides sequential composition, it becomes possible to consider the subalgebra that arises if we delete the sequential composition operator. Th... |

13 | A complete equational axiomatization for MPA with string iteration
- Aceto, Groote
- 1995
(Show Context)
Citation Context ...en a complete finite axiomatization cannot be found. This was shown by Sewell [20]. On the other hand, there are extensions of action prefix iteration that still have finite axiomatizations, see e.g. =-=[1, 15]-=-. We can look at the combination of prefix iteration and renaming. Here, the axioms we have are definitely not complete, we need the following extra axiom: # f (a # x) = f(a) # # f (x). Using this axi... |

13 |
On sequential composition, action prefixes and process prefix
- Baeten, Bergstra
- 1994
(Show Context)
Citation Context ...he signature by deleting the prefix operators. The subalgebra of the initial algebra that is obtained by this reduced signature is now completely axiomatised by the theory BPA ## of [8, 7]. Following =-=[2]-=-, we call BPA ## an SRM-specification (Subalgebra of Reduced Model Specification) of SPA. Then, we can reduce further by deleting #, or also #, and obtain the SRM specifications BPA # resp. BPA of [11... |

5 |
Grammars Modulo Bisimulation
- Bosscher
- 1997
(Show Context)
Citation Context ...e that, due to the presence of the constant #, a di#erence between SPA and the standard theory BPA is that finite guarded recursion allows the specification of a process with unbounded branching (see =-=[13]-=-). 8 The third possibility is adding still fewer constants, adding only #X|E# over the syntax of MPA. We call an equation linear if it is guarded and just uses the signature of MPA. Notice this is a v... |

5 | Axiomatizing flat iteration
- Glabbeek
- 1997
(Show Context)
Citation Context ...en a complete finite axiomatization cannot be found. This was shown by Sewell [20]. On the other hand, there are extensions of action prefix iteration that still have finite axiomatizations, see e.g. =-=[1, 15]-=-. We can look at the combination of prefix iteration and renaming. Here, the axioms we have are definitely not complete, we need the following extra axiom: # f (a # x) = f(a) # # f (x). Using this axi... |

1 |
A complete equational axiomatisation for prefix iteration
- Fokkink
- 1994
(Show Context)
Citation Context ...becomes possible to consider the subalgebra that arises if we delete the sequential composition operator. The signature of MPA (this stands for Minimal Process Algebra, this acronym was introduced in =-=[14]-=-) is the signature of SPA without sequential composition. The process algebra MPA consists of the axioms A1,2,3,6 of Table 1. Using these axioms, each closed MPA-term t can be written in one of the fo... |