## Notions of bisimulation and congruence formats (2004)

### BibTeX

@MISC{Mousavi04notionsof,

author = {Mohammad Reza Mousavi and Michel A. Reniers and Jan Friso Groote},

title = {Notions of bisimulation and congruence formats},

year = {2004}

}

### OpenURL

### Abstract

for SOS with data �

### Citations

1332 |
A Calculus of Communicating Systems
- Milner
- 1982
(Show Context)
Citation Context ...not contain a data state. Furthermore, it isM.R. Mousavi et al. / Information and Computation 200 (2005) 107–147 111 shown that the original notion of bisimilarity corresponds to strong bisimilarity =-=[26,29]-=- in the new specification. Since the resulting transition system specification is in PATH format, it is deduced that the original notion of bisimilarity is a congruence. Although the formal proof for ... |

1286 | A structural approach to operational semantics
- Plotkin
- 1981
(Show Context)
Citation Context ... SOS has been used for languages with data as an integral part of their operational state (e.g., the original report on SOS contains several examples of state-bearing transition system specifications =-=[30]-=-). As systems get more complex, the integration of a data state in their semantics becomes more vital. Besides the systems that have an explicit notion of data such as [16,11], real-time languages [4,... |

656 |
Concurrency and automata on infinite sequences
- Park
- 1981
(Show Context)
Citation Context ...not contain a data state. Furthermore, it isM.R. Mousavi et al. / Information and Computation 200 (2005) 107–147 111 shown that the original notion of bisimilarity corresponds to strong bisimilarity =-=[26,29]-=- in the new specification. Since the resulting transition system specification is in PATH format, it is deduced that the original notion of bisimilarity is a congruence. Although the formal proof for ... |

298 | Universal coalgebra: a theory of systems
- Rutten
(Show Context)
Citation Context ... is another interesting direction for our future research. We are currently investigating a bi-algebraic and categorical interpretation of notions of bisimulation with data, following the approach of =-=[37,38,35]-=-. In this article, we have only proved sufficient conditions for the notions of bisimulation with data to be a congruence. Although we have already shown that no straightforward relaxation of our form... |

194 |
Bisimulation can’t be traced
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...d the label of the conclusion. (It turns out that side conditions of this kind do not play any role on the congruence result and thus we do not mention them in the rest of this article.) Bloom et al. =-=[8]-=-, in their study of the relationship between bisimilarity and completed-trace congruence, define an extension of the De Simone format, called GSOS (for Structural Operational Semantics with Guarded re... |

189 |
Structured operational semantics and bisimulation as a congruence
- Groote, Vaandrager
- 1992
(Show Context)
Citation Context ...es only among xk’s (0 � k<n) and yij’s (i ∈ I and j � mi). Another orthogonal extension of the De Simone format, called tyft/tyxt, which allows for lookahead in the premises of a rule, is proposed in =-=[23]-=- (tyft/tyxt is the code summarizing the structure of SOS rule in this format). This format allows for arbitrary terms in the left-hand sides (called sources) of the premises and in the right-hand side... |

134 | Toward a mathematical Operational Semantics
- Turi, Plotkin
- 1997
(Show Context)
Citation Context ... is another interesting direction for our future research. We are currently investigating a bi-algebraic and categorical interpretation of notions of bisimulation with data, following the approach of =-=[37,38,35]-=-. In this article, we have only proved sufficient conditions for the notions of bisimulation with data to be a congruence. Although we have already shown that no straightforward relaxation of our form... |

121 | Structural operational semantics
- Aceto, Fokkink, et al.
- 1999
(Show Context)
Citation Context ...rted variable binding. This covers the problem of operators such as recursion or choice over a time domain. The issue of binding operators for multi-sorted process terms is also briefly introduced in =-=[2]-=-. In an unpublished note [9], the issue of state-bearing and parameterized processes is treated and a congruence format is proposed (called Super-SOS). The approach of [9] relies on transforming state... |

115 |
Transition system specifications with negative premises
- Groote
- 1993
(Show Context)
Citation Context ...f premises (with respect to the variable dependency ordering) there exists a rule that induces the same transition relation and is indeed well-founded. The merits of the two extensions were merged in =-=[20]-=- where negative premises were added to the tyft/tyxt format, resulting in the ntyft/ntyxt format. In the premises of ntyft/ntyxt rules negative transition relations of the form ti li ↛ can appear as w... |

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 ...ratification is concerned with defining a measure that decreases from the conclusion to negative premises and that does not increase from the conclusion to positive premises. Finally, the PATH format =-=[5]-=- (for Predicates And Tyft/tyxt Hybrid format) and the PANTH format [39] (for Predicates And Negative Tyft/tyxt Hybrid format) extend tyft/tyxt and ntyft/ntyxt with predicates, respectively. A deductio... |

87 | Turning SOS rules into equations
- Aceto, Bloom, et al.
- 1994
(Show Context)
Citation Context ...uence or they can be relaxed in any way. Generating equational theories from transition systems specifications is another direction of our ongoing research. Deriving algebraic axioms for SOS rules in =-=[1,3]-=- are among notable examples in this direction which try to generate a set of sound and complete axioms for a given operational semantics in a syntactic format. Both [1,3] assume the existence of a num... |

64 | Structural Operational Semantics - Plotkin - 1981 |

54 | Ntyft/ntyxt rules reduce to ntree rules
- Fokkink, Glabbeek
- 1996
(Show Context)
Citation Context .... A variable dependency graph has variables as its nodes and there exists an edge from one variable to another if the former appears in the source and the latter in the target of a premise. Later, in =-=[19]-=- it is shown that the acyclicity constraint can be relaxed and that for every tyft/tyxt rule with a non-well-founded set of premises (with respect to the variable dependency ordering) there exists a r... |

47 |
Plain CHOCS: A second generation calculus for higher order processes
- Thomsen
- 1993
(Show Context)
Citation Context ...ponent in an arbitrary system with a (bi-)similar counterpart, the resulting system is (bi-)similar to the original one. Proofs of congruence for SOS are usually standard but very tedious and lengthy =-=[18,36]-=-. This has resulted in a line of research for defining standard syntactical formats for different types of SOS in order to obtain the congruence property for a given notion of bisimilarity automatical... |

38 | R.: The meaning of negative premises in transition system specifications II
- Glabbeek
- 2004
(Show Context)
Citation Context ...of a transition is (see [20,39]). Not every transition system specification with negative premises defines a transition relation. Different interpretations of negative premises can be considered (see =-=[40]-=-), but here we adopt the interpretation put forward by [20]. A sufficient condition for the existence of a transition relation is that the transition system specification is stratifiable. A stratifica... |

36 | A congruence theorem for structured operational semantics of higherorder languages
- Bernstein
- 1998
(Show Context)
Citation Context ...ms. This allows both for more expressiveness in the specification of SOS and for the possibility of introducing new notions of equivalence (w.r.t. the relationship between data and process terms). In =-=[7]-=-, an extension of the tyft/tyxt format is proposed to cover the semantics of higher order languages. The extended format, called promoted tyft/tyxt, allows for putting (open) terms on the labels as we... |

30 |
Higher-Level Synchronizing Devices
- Simone
- 1985
(Show Context)
Citation Context ...ludes the article and presents possible extensions of the proposed approach. 2. Related work The first standard format for congruence of a transition system specification was proposed by De Simone in =-=[17]-=-. The De Simone format allows for deduction rules of the following form: {xi li → yi | i ∈ I} f(x0, ..., xn−1) l → t [P( −→ li , l)],M.R. Mousavi et al. / Information and Computation 200 (2005) 107–1... |

28 |
Reniers. Hybrid process algebra
- Cuijpers, A
- 1984
(Show Context)
Citation Context ... the integration of a data state in their semantics becomes more vital. Besides the systems that have an explicit notion of data such as [16,11], real-time languages [4,10,21,24] and hybrid languages =-=[14,6]-=- are other typical examples of systems in which a data state shows itself in the operational semantics in one way or another. However, the introduction of data turns out not to be as trivial as it see... |

27 | Process algebra for hybrid systems
- Bergstra, Middleburg
- 2005
(Show Context)
Citation Context ... the integration of a data state in their semantics becomes more vital. Besides the systems that have an explicit notion of data such as [16,11], real-time languages [4,10,21,24] and hybrid languages =-=[14,6]-=- are other typical examples of systems in which a data state shows itself in the operational semantics in one way or another. However, the introduction of data turns out not to be as trivial as it see... |

26 | The Syntax and Semantics of timed CRL
- Groote
- 1997
(Show Context)
Citation Context ...30]). As systems get more complex, the integration of a data state in their semantics becomes more vital. Besides the systems that have an explicit notion of data such as [16,11], real-time languages =-=[4,10,21,24]-=- and hybrid languages [14,6] are other typical examples of systems in which a data state shows itself in the operational semantics in one way or another. However, the introduction of data turns out no... |

20 | Axiomatizing GSOS with termination
- Baeten, Vink
(Show Context)
Citation Context ...uence or they can be relaxed in any way. Generating equational theories from transition systems specifications is another direction of our ongoing research. Deriving algebraic axioms for SOS rules in =-=[1,3]-=- are among notable examples in this direction which try to generate a set of sound and complete axioms for a given operational semantics in a syntactic format. Both [1,3] assume the existence of a num... |

20 | Bisimilarity of open terms
- Rensink
- 1997
(Show Context)
Citation Context ...n is the smallest relation containing all provable closed formulae. Note that in this paper, we only consider transition relations and notions of bisimulation on closed terms. Techniques developed in =-=[34]-=- can be used to define these concepts on open terms. 3.2. Notions of bisimilarity The introduction of data to the state adds a new dimension to the notion of bisimilarity. One might think that we can ... |

19 | Variable binding operators in transition system specifications
- Middelburg
(Show Context)
Citation Context ...s, respectively. A deduction rule in PANTH format may have predicates, negative predicates, transitions and negative transitions in its premises, and a predicate or a transition in its conclusion. In =-=[25]-=-, the PANTH format is extended for multi-sorted variable binding. This covers the problem of operators such as recursion or choice over a time domain. The issue of binding operators for multi-sorted p... |

15 | On the Expressiveness of Linda-like Concurrent Languages - Brogi, Jacquet - 1998 |

12 |
Process Algebra with Timing. EATCS Monographs
- Baeten, Middelburg
- 2002
(Show Context)
Citation Context ...30]). As systems get more complex, the integration of a data state in their semantics becomes more vital. Besides the systems that have an explicit notion of data such as [16,11], real-time languages =-=[4,10,21,24]-=- and hybrid languages [14,6] are other typical examples of systems in which a data state shows itself in the operational semantics in one way or another. However, the introduction of data turns out no... |

11 |
Separating Computation and Coordination in the Design of Parallel and Distributed Programs
- Chaudron
- 1998
(Show Context)
Citation Context ...arity in that setting [22]. Another option for open systems with a limited possibility of intervention from the environment is to parameterize the notion of bisimilarity with an interference relation =-=[22,12,14]-=-. Our congruence format for state-based bisimilarity can be adapted to the parameterized notion of bisimilarity. Next, we compare the above three notions of bisimilarity. 3.3. Comparing the notions of... |

9 | Congruence for SOS with data
- Mousavi, Reniers, et al.
- 2004
(Show Context)
Citation Context ...lsevier Inc. All rights reserved. Keywords: Formal semantics; Structural operational sematics; Bisimulation; Congruence; SOS formats � A preliminary and summarized version of this article appeared as =-=[28]-=-. ∗ Corresponding author. E-mail address: m.r.mousavi@tue.nl (M.R. Mousavi). 0890-5401/$ - see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.ic.2005.03.002108 M.R. Mousavi et a... |

8 | Process algebra with guards: Combining Hoare logic with process algebra - Groote, Ponse - 1994 |

8 | On timed coordination languages - Jacquet, Bosschere, et al. - 2000 |

5 | Separating functionality, behavior and timing in the design of reactive systems: (GAMMA + coordination) + time
- Mousavi, Basten, et al.
- 2002
(Show Context)
Citation Context ...he operational semantics in one way or another. However, the introduction of data turns out not to be as trivial as it seems and leads to new semantical issues such as adapted notions of bisimilarity =-=[10,21,14,27]-=-. To the best of our knowledge, no standard congruence format for these different notions of bisimilarity with a data state has been proposed so far. Hence, most of the congruence proofs are done manu... |

4 | SOS rule formats for parameterized and state-bearing processes
- Bloom, Vaandrager
- 1994
(Show Context)
Citation Context .... Hence, most of the congruence proofs are done manually [27] or are just neglected by making a reference to a standard format that does not cover the data state [10]. The proposal that comes closest =-=[9]-=- is unfinished and encodes rules for state-bearing processes into rules without a state, for which a format is given. In this article, we address the implications of the presence of a data state on th... |

4 | A behavioural theory of first-order CML
- Ferreira, Hennessy
- 1999
(Show Context)
Citation Context ...ponent in an arbitrary system with a (bi-)similar counterpart, the resulting system is (bi-)similar to the original one. Proofs of congruence for SOS are usually standard but very tedious and lengthy =-=[18,36]-=-. This has resulted in a line of research for defining standard syntactical formats for different types of SOS in order to obtain the congruence property for a given notion of bisimilarity automatical... |

3 | Action and predicate safety of hybrid processes
- Cuijpers, Reniers
- 2004
(Show Context)
Citation Context ... ∂H (y) , ′ (x, ) ̌ (∂H (x) , ) ̌ . On HyPA process terms, in [14], a notion of robust bisimilarity is defined that, for HyPA, coincides with our definition of stateless bisimilarity. Furthermore, in =-=[13]-=-, for the purpose of analyzing sequential HyPA processes (i.e., HyPA processes without operators for parallel composition), a notion of bisimilarity is defined that coincides with our notion of initia... |

2 |
Redesign of a systems engineering language––formalisation of χ, Formal Aspects of Computing 15
- Bos, Kleijn
- 2003
(Show Context)
Citation Context ...30]). As systems get more complex, the integration of a data state in their semantics becomes more vital. Besides the systems that have an explicit notion of data such as [16,11], real-time languages =-=[4,10,21,24]-=- and hybrid languages [14,6] are other typical examples of systems in which a data state shows itself in the operational semantics in one way or another. However, the introduction of data turns out no... |

2 |
de Vink, Control Flow Semantics. Foundations of Computing Series
- Bakker, P
- 1996
(Show Context)
Citation Context ...ition system specifications [30]). As systems get more complex, the integration of a data state in their semantics becomes more vital. Besides the systems that have an explicit notion of data such as =-=[16,11]-=-, real-time languages [4,10,21,24] and hybrid languages [14,6] are other typical examples of systems in which a data state shows itself in the operational semantics in one way or another. However, the... |

1 |
Functorial operational semanticsand its denotational dual
- Turi
(Show Context)
Citation Context ... is another interesting direction for our future research. We are currently investigating a bi-algebraic and categorical interpretation of notions of bisimulation with data, following the approach of =-=[37,38,35]-=-. In this article, we have only proved sufficient conditions for the notions of bisimulation with data to be a congruence. Although we have already shown that no straightforward relaxation of our form... |