## Transition System Specifications in Stalk Format With Bisimulation as a Congruence (1994)

Venue: | in Proceedings 11th Symposium on Theoretical Aspects of Computer Science |

Citations: | 1 - 0 self |

### BibTeX

@INPROCEEDINGS{Oostrom94transitionsystem,

author = {Van Oostrom and E. P. De Vink},

title = {Transition System Specifications in Stalk Format With Bisimulation as a Congruence},

booktitle = {in Proceedings 11th Symposium on Theoretical Aspects of Computer Science},

year = {1994},

pages = {569--580},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

A many-sorted variant, called stalk format, of the single sorted tyft-format for transition system specifications, introduced by Groote and Vaandrager, is proposed. The stalk format is shown to be a convenient formalism to express continuation-style transition systems for languages incorporating concepts as, e.g., process creation or backtracking, for which the existing formats seem less adequate. It is proved, extending a similar result for the single sorted case, that for an appropriate generalization of (strong) bisimilarity for the present many-sorted setting, bisimulation with respect to a transition system specification in stalk format, is a congruence. It is argued that the several conditions, required for the type of transition system specification put forward in the paper, can not be relaxed without loosing this congruence. Finally, the present format is compared with several existing ones in the literature, viz. De Simone-, GSOS- and pure tyft-format. Keywords and phrases se...

### Citations

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Citation Context ...description itself, the axioms and rules, a transition system specification. Presently, all core example languages for concurrency theory have been given an operational semantics using SOS, e.g., CCS =-=[Mil80]-=-, TCSP [OH86], ACP [Gla87] and Meije [Bou85] and many more variants and extensions. However, the general theory of transition system specifications has, compared to the bulk of the applications, attra... |

1385 | A structural approach to operational semantics
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Citation Context ...em specifications, bisimulation equivalence 1 Introduction In providing an operational semantics for programming language concepts the Structural Operational Semantics (SOS) or Plotkin-style approach =-=[Plo81]-=- based on labeled transition systems is likely to be the most widely used technique. The behavior of an abstract machine executing the language under consideration is described using a set of syntax-d... |

432 | Bisimulation through probabilistic testing - Larsen, Skou - 1991 |

201 |
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Citation Context ...ity condition on the variables of t, and, more particularly, satisfies var (t) ` f z 1 ; : : : z ` g where z k j x k if k = 2 I and z k j y k otherwise. The form of a GSOS rule or, as it is called in =-=[BIM88]-=-, a Structured Transition Rule is the following x k a ij ! y ij (i 2 I; j 2 J) x k b ik 9 (i 2 I 0 ; k 2 K) f(x 1 ; : : : ; x ` ) a ! t where x i , y ij (1sks`; j 2 J) are all different variables I; I... |

201 |
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Citation Context ...s for such concepts as process creation and backtracking fit neatly within the stalk format. As will be discussed below in Section 5, the stalk format does not precisely generalize the tyft format of =-=[GV92]-=- due to the absence of lookahead. A technical condition on variable occurrences, necessitated by the proof of the congruence theorem, prohibits the stalk format of having such a facility. However, the... |

133 |
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Citation Context ... for some bisimulation `'. Property 2.5 Let T and A be sets and ! ` T \Theta A \Theta T. (a) $ = S fs` T 2 j `' a bisimulationg is a bisimulation relation. (b) $ is an equivalence relation. Proof See =-=[Mil90]-=-. 2 3 The stalk format In this section we introduce a special kind of many-sorted signatures, called layered signature, in which the set of sorts is partially ordered. On the basis of the ordering of ... |

121 | Transition system specifications with negative premises - Groote - 1993 |

86 |
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Citation Context ...self, the axioms and rules, a transition system specification. Presently, all core example languages for concurrency theory have been given an operational semantics using SOS, e.g., CCS [Mil80], TCSP =-=[OH86]-=-, ACP [Gla87] and Meije [Bou85] and many more variants and extensions. However, the general theory of transition system specifications has, compared to the bulk of the applications, attracted little a... |

74 | The meaning of negative premises in transition system specifications - Bol, Groote - 1996 |

67 | Higher-level synchronising devices in MEIJE–SCCS - Simone - 1985 |

50 |
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Citation Context ...ere is no direct relationship between our use of the ordering `' of the sorts for a layered signature (\Sigma; ) and the use of an ordering for the notion of an order-sorted signature in the sense of =-=[SNGM89]-=-. Definition 3.3 Let (\Sigma; ) be a layered signature. (a) A stalk is a context C[\Delta] with function symbols only from the root to the hole (considering a term as a downward rooted tree). (b) A st... |

37 | Comparative Semantics for Prolog with Cut - Vink - 1989 |

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Citation Context ...transition system specification. Presently, all core example languages for concurrency theory have been given an operational semantics using SOS, e.g., CCS [Mil80], TCSP [OH86], ACP [Gla87] and Meije =-=[Bou85]-=- and many more variants and extensions. However, the general theory of transition system specifications has, compared to the bulk of the applications, attracted little attention. Apart from some compa... |

33 |
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Citation Context ...ioms and rules, a transition system specification. Presently, all core example languages for concurrency theory have been given an operational semantics using SOS, e.g., CCS [Mil80], TCSP [OH86], ACP =-=[Gla87]-=- and Meije [Bou85] and many more variants and extensions. However, the general theory of transition system specifications has, compared to the bulk of the applications, attracted little attention. Apa... |

30 |
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Citation Context ...t less than S i , the type of u i ; v i .) Using the transitivity of $ we derive C[f(u 1 ; : : : ; u k )] $ C[f(v 1 ; : : : ; v k )]. Hence f(u 1 ; : : : ; u k ) [] f(v 1 ; : : : ; v k ). (Cf., e.g., =-=[Wec92]-=-, Sc. 2.1.2 for a similar type of argument.) In general, the notion of contextual bisimilarity, as given in Definition 4.1, is not always a congruence. However, the main objection against the adaptati... |

22 | Readies and failures in the algebra of communicating processes - Bergstra, Klop, et al. - 1988 |

22 |
Processes as terms: non-well-founded models for bisimulation
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Citation Context ...he variables x 1 ; : : : ; x ` or, otherwise, may already have occurred as right-hand side of a premise. (This is a rephrasing of the inductivity requirement in the presentation of the tyft format in =-=[Rut92]-=-.) Thus a rule of the form, taken from [BK88], x a 1 ! x 1 x 1 a 2 ! x 2 : : : x n an ! E [x] a ! E where x; x 1 ; : : : ; x n are variables, E is a constant and [\Delta] is unary function symbol, is ... |

17 | A Parallel Object-Oriented Language : Design and Semantic Foundations - America, Rutten - 1989 |

17 | Comparative semantics for flow of control in logic programming without logic - Bakker - 1991 |

16 | The tyft/tyxt format reduces to tree rules
- Fokkink
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Citation Context ...tain tree-like contexts replacing smooth stalk in the definition of the format. Also, such questions as finite vs. infinite expressibility as in an issue in comparing the tree rule and tyft format in =-=[Fok93]-=- should be considered. Furthermore, related decidability and termrewriting questions should be explored. A final direction into which to extend the research concerns the derivation of denotational sem... |

11 |
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(Show Context)
Citation Context ...may already have occurred as right-hand side of a premise. (This is a rephrasing of the inductivity requirement in the presentation of the tyft format in [Rut92].) Thus a rule of the form, taken from =-=[BK88]-=-, x a 1 ! x 1 x 1 a 2 ! x 2 : : : x n an ! E [x] a ! E where x; x 1 ; : : : ; x n are variables, E is a constant and [\Delta] is unary function symbol, is permitted in the tyft format. This feature, r... |

11 |
An algebra for process creation
- Baeten, Vaandrager
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(Show Context)
Citation Context ...of completed trace congruences in terms of a special bisimulation would facilitate the comparison with general GSOS and pure tyft. On the other hand, for particular cases it seems possible, following =-=[BV92a]-=- to discard the many sortedness of the format. It therefore may very well be the case that the restrictions of the format (contexts in the shape of smooth stalks) can be relaxed. Also, if the congruen... |

10 | Structural operational specifications and trace automata - Badouel, Darondeau - 1992 |

9 | Bisimulation Semantics for Concurrency with Atomicity and Action Refinement - Bakker, Vink - 1994 |

8 |
Deriving denotational models for bisimulation from structured operational semantics, in
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(Show Context)
Citation Context ...ability and termrewriting questions should be explored. A final direction into which to extend the research concerns the derivation of denotational semantics from transition system specifications. In =-=[Rut90a]-=- such a construction is achieved in a setting of metric spaces for the De Simone format. In [Rut92] this is extended, in a setting of non-wellfounded sets, to the (image finite) tyft-format. In both c... |

5 |
Calculabilit'e et expressivit'e dans l'algebra de processus parall`eles MEIJE
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Citation Context ...pecification T bpa over the single-sorted signature \Sigma bpa of Example 2.2 is in stalk format. The only stalk involved is the empty context. (In fact, T bpa is in the so-called De Simone format of =-=[Sim84]-=-, which is a special subcase of a transition system specification in stalk format. See Section 5.) 6 Example 3.7 For a more illustrative example we turn to a simple uniform language with process creat... |

3 | Designing Equivalent Models for Process Creation - America, Bakker - 1988 |

2 | Trace nets - Badouel, Darondeau - 1993 |

2 | Rendez-vous with metric semantics - Bakker, Vink - 1991 |

2 | Semantic correctness for a parallel object-oriented language - Rutten - 1990 |

1 | Continuation semantics for Prolog with cut (extended abstract - Bruin, Vink - 1989 |

1 | Asynchronous rendez-vous in Distributed Logic Programming - Eliens, Vink - 1993 |