## Formats of Ordered SOS Rules with Silent Actions (1997)

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Venue: | Proceedings 7th Conference on Theory and Practice of Software Development (TAPSOFT'97), Lille, LNCS 1214 |

Citations: | 7 - 3 self |

### BibTeX

@INPROCEEDINGS{Ulidowski97formatsof,

author = {Irek Ulidowski and Iain Phillips},

title = {Formats of Ordered SOS Rules with Silent Actions},

booktitle = {Proceedings 7th Conference on Theory and Practice of Software Development (TAPSOFT'97), Lille, LNCS 1214},

year = {1997},

pages = {297--308},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

We present a general and uniform method for defining structural operational semantics (SOS) of process algebra operators by traditional Plotkin-style rules equipped with an ordering, the new feature which states the order of application of rules when deriving transitions of process terms. Our method allows to represent negative premises and copying in the presence of silent actions. We identify a number of general formats of unordered and ordered rules with silent actions and show that divergence sensitive branching and weak bisimulation relations are preserved by all operators in the relevant formats. A comparison with the existing formats for branching and weak bisimulations shows that our formats are more general.

### Citations

3203 |
Communication and concurrency
- Milner
- 1989
(Show Context)
Citation Context ...ely defined by De Simone rules alone. The most important examples of these are, on one hand, sequential composition and priority operators and, on the other hand, replication and checkpoint operators =-=[Mil89]-=-. Such operators are usually defined by rules with negative premises (expressions like X a 9) and copying (multiple use of identical process variables) respectively. In order to provide for such opera... |

1329 | A calculus of communicating systems - Milner - 1980 |

1286 | A structural approach to operational semantics
- Plotkin
- 1981
(Show Context)
Citation Context ...ered to be the standard method for defining the operational meaning of process operators in an arbitrary process language. It was originated by Milner for CCS [Mil80, Mil89] and formalised by Plotkin =-=[Plo81]-=-. The meaning of each operator on processes is given by a set of transition rules. Each rule describes how the behaviour of a process, constructed with the operator and some subprocesses, depends on t... |

255 | Branching Time and Abstraction in Bisimulation Semantics - Glabbeek, Weijland - 1996 |

194 | Bisimulation can’t be traced - Bloom, Istrail, et al. - 1995 |

189 | Structured operational semantics and bisimulation as a congruence - Groote, Vaandrager - 1992 |

115 |
Transition system specifications with negative premises
- Groote
- 1993
(Show Context)
Citation Context ...g ! specifies that a rule can only be applied when no rules with a higher priority can be applied. Next, we describe how to associate a transition relation with a given (G; !) 2 . We take a lead from =-=[Gro93]-=-. Let d : T(\Sigma) ! N be a function which specifies the depth of operator names in a ground term over a signature \Sigma. Function d is defined inductively as follows: d(t) = 0 if t is a constant, a... |

111 | A Process Algebra for Timed Systems - Hennessy, Regan - 1995 |

87 | Turning SOS rules into equations - Aceto, Bloom, et al. - 1994 |

74 |
Syntax and defining equations for an interrupt mechanism in process algebra
- Baeten, Bergstra, et al.
(Show Context)
Citation Context ... ifsi ! r and i 2 active(r 0 ) then r 6jsi and r 0 ! r (4) However, there are operators definable by bb rules satisfying condition (4) which are not well behaved. Consider the priority operator ` (cf =-=[BBK86]-=-) which gives d priority over b. It is defined by the rule schema r ff below, for ff 2 fb; dg, with the -rules1 and the ordering r b ! r d . X ff ! X 0 r ff `(X) ff ! `(X 0 ) Let p = b:0 k :d:0 and q ... |

64 | Observation equivalence as a testing equivalence - Abramsky - 1987 |

57 |
Comparative concurrency semantics and refinement of actions
- Glabbeek
- 1990
(Show Context)
Citation Context ...which replaces all occurrences of an action by some process. It is known that for purely sequential processes action refinement preserves branching bisimulation but not the standard weak bisimulation =-=[vG90]-=-. Below, we define a wbo version of action refinement operator refine-a such that refine-a(p; q) refines all a in p by q. Our operator differs from the one described in [vG90] in that when refine-a(p;... |

53 | Bisimulation can’t be traced: Preliminary report - Bloom, Istrail, et al. - 1989 |

47 |
Refusal testing
- Phillips
- 1987
(Show Context)
Citation Context ...ot increase. This result will help to prove the congruence results for branching and weak bisimulation preorders We recall that action refusal is the inability to perform the action in a stable state =-=[Phi87]-=-. Process p refuses to perform action ff, written as p ~ ff !, if p is stable, namely p 9, and p ff 9. Let, ~ Act denote the set action refusals associated with Act, namely f~ff j ff 2 Actg. Also, let... |

47 | Bisimulations and divergence - Walker - 1988 |

43 |
Structural operational semantics for weak bisimulations
- Bloom
- 1995
(Show Context)
Citation Context ...ple formats for slightly non-standard, but possibly more suitable, equivalences. The first approach was followed in [Blo90b, Vaa91, Blo95]. For example, one of the equivalences considered by Bloom in =-=[Blo95]-=- is the rooted version of weak bisimulation (or observational congruence) [Mil89, BW90], but the discovered format came out quite complicated. On the other hand, formats for branching bisimulation-lik... |

39 | On the relationship between process algebra and input/output automata
- Vaandrager
- 1991
(Show Context)
Citation Context ...perators which are definable in these formats do not preserve the considered equivalences. Formats of rules with positive premises and silent actions were studied by Bloom [Blo90b, Blo95], Vaandrager =-=[Vaa91]-=- and the first author [Uli92, Uli94], who also considered rules with negative premises. A common feature of these approaches was to represent the traditional character of silent actions via -rules whi... |

35 |
Higher-level synchronising devices
- Simone
- 1985
(Show Context)
Citation Context ...rmat if its rules belong to that format. Moreover, a process language is in a certain format if all its operators are in that format. Most of the popular process operators are in the De Simone format =-=[dS85]-=-. However, De Simone rules have rather restricted form. They do not make use of either the negative behaviour 1 of subprocesses, namely the inability to perform actions, or the branching behaviour of ... |

32 | Deriving complete inference systems for a class of GSOS languages generating regular behaviours - Aceto - 1994 |

21 | A modal characterisation of observable machine behaviour - Milner |

20 | Ready Simulation, Bisimulation, and the Semantics of CCS-like Languages - Bloom - 1989 |

19 | Equivalences on observable processes
- Ulidowski
- 1992
(Show Context)
Citation Context ...acter of silent actions yet. We additionally insist that silent actions are unobservable: silent actions of subprocesses cannot produce a visible behaviour of the process or a change in its structure =-=[Uli92]-=- 3 . This principle can be formulated as follows: ifs2 actions(r) then r is a -rule (2) meaning that no rules except -rules can havesactions in the premises. This will disallow operators like see- , d... |

13 | Synchrony and asynchrony in process algebra - WEIJLAND - 1989 |

11 | A Calculus of Real Time Systems - Wang - 1991 |

9 |
Strong process equivalence in the presence of hidden moves
- Bloom
- 1990
(Show Context)
Citation Context ...li94], who also considered rules with negative premises. A common feature of these approaches was to represent the traditional character of silent actions via -rules which were originally proposed in =-=[Blo90b]-=-. The motivation for -rules is as follows: if f is n-ary operator and the behaviour of f(X) depends on the behaviour of its component X i then when X i evolves silently f(X) can do nothing else but to... |

8 |
Local testing and implementable concurrent processes
- Ulidowski
- 1994
(Show Context)
Citation Context ...o95]. The second approach was followed by the first author who defined the ISOS format [Uli92, Uli94], the most general format so far with silent actions, negative premises and copying. It was proved =-=[Uli94]-=- that not the standard weak bisimulation but a slightly finer, divergence sensitive version of weak bisimulation, studied in [Mil81, Abr87, Wal90], is preserved by ISOS operators. In this paper we ado... |

6 | CPO models for a Class of GSOS languages
- Aceto, Ingolfsdottir
- 1995
(Show Context)
Citation Context ...h includes congruence results for strong bisimulation and ready simulation [BIM88, Blo90a, BIM95], procedures for automatic generation of complete axiom systems [ABV94, Ace94] and denotational models =-=[AI95]-=-. An important problem concerning formats of transition rules is how to use silent actions in rules. Original De Simone and GSOS formats treat both silent and visible actions in the same way, namely a... |

4 |
Approaches to priority in process algebra
- Phillips
- 1994
(Show Context)
Citation Context ... `(X) ! `(X 0 ) Let the ordering be such that (1) r a ! r b whenever a ! b and (2)s1 ? r b , for each b, whenever there exist a rule r a such that r a 2 higher(r b ). Clearly, ` is a wbo operator. In =-=[Phi94]-=-, the second author surveyed a number of approaches to priorities in process algebras. He showed how these approaches may be fitted into a common operational framework based on ordered rules. 17 The n... |

4 | Ordered SOS rules and weak bisimulation
- Phillips, Ulidowski
- 1996
(Show Context)
Citation Context .... 1.1 Results We present a general method for defining process operators by Plotkin-style rules (with no negative premises) which are equipped with an ordering. Our method was informally described in =-=[PU96]-=- and further improved in [UP97]. The ordering on rules indicates the order in which rules are applied when deriving transitions of process terms. The behaviour of a process f(p) can be determined by e... |