## Discrete Time Process Algebra with Silent Step (2000)

Citations: | 16 - 7 self |

### BibTeX

@MISC{Baeten00discretetime,

author = {J.C.M. Baeten and J.A. Bergstra and M.A. Reniers},

title = {Discrete Time Process Algebra with Silent Step},

year = {2000}

}

### Years of Citing Articles

### OpenURL

### Abstract

The axiom system ACP of [10] was extended to discrete time in [6]. Here, we proceed to define the silent step in this theory in branching bisimulation semantics [7, 15] rather than weak bisimulation semantics [11, 20]. The version using relative timing is discussed extensively, versions using absolute and parametric timing are presented in brief. A term model and a graph model are presented and soundness and completeness results are given. The time free theories BPA # and BPA # # are embedded in the discrete time theories. Examples of the use of the relative time theory are given by means of some calculations on communicating buffers. Note: Partial support received from ESPRIT Basic Research Action 7166, CONCUR2. This paper supersedes [4]. 1 Introduction Process algebra was introduced by Milner in the form of CCS [19]. The original design of CCS and of subsequent versions of process algebra such as ACP [10] and TCSP [14] involves no explicit notion of time. Time is present in the int...

### Citations

3396 | Communicating sequential processes
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- 1978
(Show Context)
Citation Context ...per supersedes [4]. 1 Introduction Process algebra was introduced by Milner in the form of CCS [19]. The original design of CCS and of subsequent versions of process algebra such as ACP [10] and TCSP =-=[14]-=- involves no explicit notion of time. Time is present in the interpretation of sequential composition: in p· q (ACP notation) the process p should be executed before q. Process algebras can be introdu... |

1328 |
A Calculus of Communicating Systems
- Milner
- 1980
(Show Context)
Citation Context ...nicating buffers. Note: Partial support received from ESPRIT Basic Research Action 7166, CONCUR2. This paper supersedes [4]. 1 Introduction Process algebra was introduced by Milner in the form of CCS =-=[19]-=-. The original design of CCS and of subsequent versions of process algebra such as ACP [10] and TCSP [14] involves no explicit notion of time. Time is present in the interpretation of sequential compo... |

360 | Process algebra for synchronous communication
- Bergstra, Klop
- 1984
(Show Context)
Citation Context ...msterdam, Kruislaan 403, NL-1098 SJ Amsterdam, The Netherlands and Department of Philosophy, Utrecht University, Heidelberglaan 8, NL-3584 CS Utrecht, The Netherlands Abstract The axiom system ACP of =-=[10]-=- was extended to discrete time in [6]. Here, we proceed to define the silent step in this theory in branching bisimulation semantics [7, 15] rather than weak bisimulation semantics [11, 20]. The versi... |

254 | W.P.: Branching time and abstraction in bisimulation semantics
- Glabbeek, Weijland
- 1996
(Show Context)
Citation Context ...4 CS Utrecht, The Netherlands Abstract The axiom system ACP of [10] was extended to discrete time in [6]. Here, we proceed to define the silent step in this theory in branching bisimulation semantics =-=[7, 15]-=- rather than weak bisimulation semantics [11, 20]. The version using relative timing is discussed extensively, versions using absolute and parametric timing are presented in brief. A term model and a ... |

217 |
Algebra of communicating processes with abstraction, Theoretical Computer Science 37
- Bergstra, Klop
- 1985
(Show Context)
Citation Context ... system ACP of [10] was extended to discrete time in [6]. Here, we proceed to define the silent step in this theory in branching bisimulation semantics [7, 15] rather than weak bisimulation semantics =-=[11, 20]-=-. The version using relative timing is discussed extensively, versions using absolute and parametric timing are presented in brief. A term model and a graph model are presented and soundness and compl... |

172 |
A temporal calculus of communicating systems
- Moller, Tofts
- 1990
(Show Context)
Citation Context ...tandardized features to incorporate a quantitative view on time. Time may be represented by means of non-negative reals, and actions can be given time stamps. This line is followed in [1] for ACP, in =-=[21]-=- for CCS and in [23] for CSP. A second option is to divide time in slices indexed by natural numbers, to have an implicit or explicit time stamping mechanism that determines for each action the time s... |

156 | A timed model for communicating sequential processes
- Reed, Roscoe
- 1988
(Show Context)
Citation Context ... to incorporate a quantitative view on time. Time may be represented by means of non-negative reals, and actions can be given time stamps. This line is followed in [1] for ACP, in [21] for CCS and in =-=[23]-=- for CSP. A second option is to divide time in slices indexed by natural numbers, to have an implicit or explicit time stamping mechanism that determines for each action the time slice in which it occ... |

155 | Real time process algebra
- Baeten, Bergstra
- 1991
(Show Context)
Citation Context ...d that support standardized features to incorporate a quantitative view on time. Time may be represented by means of non-negative reals, and actions can be given time stamps. This line is followed in =-=[1]-=- for ACP, in [21] for CCS and in [23] for CSP. A second option is to divide time in slices indexed by natural numbers, to have an implicit or explicit time stamping mechanism that determines for each ... |

108 | A congruence theorem for structured operational semantics with predicates and negative premises. Nordic Journal of Computing 2 (2), 274–302. A. Proof of Theorem 9 We show that the problem of deciding whether a universal two-counter machine diverges on inp
- Verhoef
- 1995
(Show Context)
Citation Context ...most one σ-step: in a transition system, each node has at most one outgoing σ-edge. The operational semantics in Table 3 uses predicates and negative premises. Still, using terminology and results of =-=[25]-=-, the rules satisfy the panth format, and determine a unique transition relation on closed process expressions. Due to the presence of the immediate deadlock constant we have a notion of bisimulation ... |

105 | The algebra of timed processes ATP: theory and application
- Nicollin, Sifakis, et al.
- 1994
(Show Context)
Citation Context ...e an implicit or explicit time stamping mechanism that determines for each action the time slice in which it occurs and to have a time order within each slice only. This line has been followed in ATP =-=[22]-=-, a process algebra that adds time slicing to a version of ACP based on action prefixing rather than sequential composition. Further, [16] has extended ACP with time slices whereas [21] have added the... |

102 | A temporal process algebra
- Hennessy, Regan
- 1995
(Show Context)
Citation Context ...elayable actions: the action must occur before the next clock tick. The operators are alternative and sequential composition, and the relative discrete time unit delay σrel (the notation σ taken from =-=[17]-=-). The process σrel(x) will start x after one clock tick, i.e., in the next time slice. In addition, we add the auxiliary operator νrel. This operator, called the current slice time out operator, or c... |

37 |
The discrete time toolbus
- Bergstra, Klint
- 1995
(Show Context)
Citation Context ...on using parametric timing, that integrates the relative and absolute timing versions. There are many practical uses conceivable for timed process algebras. In particular, we mention the TOOLBUS (see =-=[9]-=-). This TOOLBUS contains a program notation called T which is syntactically sugared discrete time process algebra. Programs in T are called T -scripts. The runtime system is also described in terms of... |

33 | Branching bisimilarity is an equivalence indeed - Basten - 1996 |

20 |
Models and Axioms for a Fragment of Real Time Process Algebra
- Klusener
- 1993
(Show Context)
Citation Context ...ilent step. Van Glabbeek and Weijland [15] introduced branching bisimulation which also deals with silent step, but is slightly less abstract. This will allow a notion of abstraction. We mention that =-=[18]-=- has extended ACPρ, the real time ACP of [1], with silent steps. We present three views on discrete time process algebra with silent step: a version using relative timing (which we discuss extensively... |

16 |
Discrete time process algebra with abstraction
- Baeten, Bergstra
- 1995
(Show Context)
Citation Context ...use of the relative time theory are given by means of some calculations on communicating buffers. Note: Partial support received from ESPRIT Basic Research Action 7166, CONCUR2. This paper supersedes =-=[4]-=-. 1 Introduction Process algebra was introduced by Milner in the form of CCS [19]. The original design of CCS and of subsequent versions of process algebra such as ACP [10] and TCSP [14] involves no e... |

14 | Process algebra semantics of 'SDL - Bergstra, Middelburg - 1995 |

13 |
On sequential composition, action prefixes and process prefix
- Baeten, Bergstra
- 1994
(Show Context)
Citation Context ...n a theory without immediate deadlock the law x + cts(δ) = x will hold. The standard process algebra BPAδ can be considered as an SRM specification (Subalgebra of Reduced Model, in the terminology of =-=[3]-=-) of BPA − drt : consider the initial algebra of BPA− drt , reduce the signature by omitting ˙δ, σrel, νrel, then BPAδ is a complete axiomatization of the reduced model, under the interpretation of a,... |

12 |
Discrete time process algebra (extended abstract
- Baeten, Bergstra
- 1992
(Show Context)
Citation Context ...time slicing to a version of ACP based on action prefixing rather than sequential composition. Further, [16] has extended ACP with time slices whereas [21] have added these features to CCS. Following =-=[2, 6]-=-, we use the phrase discrete time process algebra if an enumeration of time slices is used. The objective of this paper is to extend the discrete time process algebra of ACP as given in [6] with the s... |

10 | Specification and Verification of Real Time Systems in acp - Groote - 1990 |

5 | Completeness in discrete-time process algebra. Computing Science
- Reniers, Vereijken
- 1996
(Show Context)
Citation Context ...unts to the presence of a new constant cts(τ) with the same axioms as the cts(a) constants. We write Aτ = A ∪ {τ}, Aδ = A ∪ {δ}, etc. The axioms DRT3 and DRT5 are derivable from the other axioms (see =-=[24]-=-). Note that x + cts(δ) = x for all closed terms x except those that are derivably equal to ˙δ (see Proposition 2.1.7), which implies that in a theory without immediate deadlock the law x + cts(δ) = x... |

3 | The I 2 C-bus in discrete-time process algebra
- BOS, RENIERS
- 1996
(Show Context)
Citation Context ...f SDL that leaves out modularization and concentrates on timing aspects (see [12]). Discrete-time process algebra with relative timing has also been used for the formal specification of the I 2 C-bus =-=[13]-=-. At this point we are happy to express our admiration for Milner’s contributions. In process theory, but not just there, he has guided the work in such directions, that the perspective of relevance a... |

3 | The I C-bus in discrete-time process algebra - Bos, Reniers - 1996 |

2 |
A process algebra semantics of φSDL
- Bergstra, Middelburg
- 1995
(Show Context)
Citation Context ...me process algebra that is used to describe T -scripts has also been used for the description of φSDL, flat SDL, a subset of SDL that leaves out modularization and concentrates on timing aspects (see =-=[12]-=-). Discrete-time process algebra with relative timing has also been used for the formal specification of the I 2 C-bus [13]. At this point we are happy to express our admiration for Milner’s contribut... |

1 | Some simple calculations in relative discrete time process algebra
- Baeten, Bergstra
- 1995
(Show Context)
Citation Context ...on, we give some simple calculations in order to illustrate the use of our discrete time theory. In the setting with unbounded start delay instead of time iteration these calculations can be found in =-=[5]-=-. We keep formulas compact by writing a instead of cts(a) and a instead of ats(a) (this is in line with notation used in [2, 13]). The communication format follows the so-called standard communication... |