## Rooted branching bisimulation as a congruence (2000)

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Venue: | Journal of Computer and System Sciences |

Citations: | 15 - 6 self |

### BibTeX

@ARTICLE{Fokkink00rootedbranching,

author = {Wan Fokkink},

title = {Rooted branching bisimulation as a congruence},

journal = {Journal of Computer and System Sciences},

year = {2000},

volume = {60},

pages = {13--37}

}

### Years of Citing Articles

### OpenURL

### Abstract

This article presents a congruence format, in structural operational semantics, for rooted branching bisimulation equivalence. The format imposes additional requirements on Groote’s ntyft format. It extends an earlier format by Bloom with standard notions such as recursion, iteration, predicates, and negative premises. 1

### Citations

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Communication and Concurrency
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Citation Context ...a, four so-called weak equivalences Supported by a grant from The Nuffield Foundation 1 have been developed to abstract away from internal machine behavior, represented by a silent steps: observation =-=[27]-=-, branching [22], delay [26], and j [3]. This article focuses on branching bisimulation equivalence, in which one can abstract away from an actionsif its execution does not implicate the loss of possi... |

1492 | The stable model semantics for logic programming
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Citation Context ...e N= where N contains only negative transitions and C j= N . 4 Each TSS T allows an (information-)least three-valued stable model hC; Ui, in the sense that the set U is maximal. Gelfond and Lifschitz =-=[15]-=- studied two-valued stable models, which are three-valued stable models for which the set of unknown positive transitions is empty. Van Glabbeek [21] introduced the notion of a complete TSS. Definitio... |

1286 | A structural approach to operational semantics
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- 1981
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Citation Context ... on Groote's ntyft format. It extends an earlier format by Bloom with standard notions such as recursion, iteration, predicates, and negative premises. 1 Introduction Structural operational semantics =-=[29]-=- has evolved as a standard methodology to provide specification languages, programming languages, and process algebras with a semantics. In structural operational semantics, transitions with action la... |

844 | The well-founded semantics for general logic programs
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- 1991
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Citation Context ...hree-valued stable model in which the set of transitions in limbo is maximal; this so-called least three-valued stable model coincides with the well-founded semantics of van Gelder, Ross, and Schlipf =-=[14]-=-. A TSS is complete [21] (or positive after reduction [10]) if all transitions in its least three-valued stable model are either true or false. Although in general it is not effectively decidable whet... |

655 |
Concurrency and automata on infinite sequences
- Park
- 1981
(Show Context)
Citation Context ...f behavioral equivalences, to avoid repetitive congruence proofs, and to explore the boundaries for transition rules that constitute sensible semantic definitions. For strong bisimulation equivalence =-=[28]-=-, Groote [23] defined the ntyft format (extending the earlier GSOS [9] and tyft [24] formats), which incorporates negative premises. Bol and Groote [10] proved that if a TSS is complete and in the nty... |

529 |
A lattice-theorethic Fixpoint Theorem and its applications
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- 1955
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Citation Context ...following two inclusions can be derived for ordinals ff and fi with fisff, by ordinal induction (cf. [13]): 1. C fi ` C ff ; 2. U fi ' U ff . Owing to these two inclusions, the Knaster-Tarski theorem =-=[33]-=- yields that there exists an ordinalssuch that Cs= C +1 and Us= U +1 . It is easy to see that hCs; Usi is a three-valued stable model for T (owing to the definitions ofs2 C +1 ands2 C +1 [ U +1 ). Fur... |

376 |
Representation of events in nerve nets and finite automata
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- 1951
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Citation Context ...o three open questions that were posed by Bloom in the conclusion of his paper. We give several examples of operators from the literature that are RBB safe but not RBB cool: recursion [16], iteration =-=[25]-=-, empty process [39], and a weaker version of the priority operator [1]. Section 3.4 contains counter-examples to show that the syntactic requirements of the RBB safe format are all essential. Finally... |

289 | The linear time - branching time spectrum
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- 1990
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Citation Context ...tion [23, 31] provides a convenient method to decide for many TSSs in the literature that they are complete. Labeled transition systems can be distinguished by a wide range of behavioral equivalences =-=[17, 18]-=-. In the field of process algebra, four so-called weak equivalences Supported by a grant from The Nuffield Foundation 1 have been developed to abstract away from internal machine behavior, represented... |

255 | Branching Time and Abstraction in Bisimulation Semantics
- Glabbeek, Weijland
- 1996
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Citation Context ...d weak equivalences Supported by a grant from The Nuffield Foundation 1 have been developed to abstract away from internal machine behavior, represented by a silent steps: observation [27], branching =-=[22]-=-, delay [26], and j [3]. This article focuses on branching bisimulation equivalence, in which one can abstract away from an actionsif its execution does not implicate the loss of possible behavior. In... |

254 |
On the declarative semantics of deductive databases and logic programs
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Citation Context ...[10]) if all transitions in its least three-valued stable model are either true or false. Although in general it is not effectively decidable whether a TSS is complete, the notion of a stratification =-=[23, 31]-=- provides a convenient method to decide for many TSSs in the literature that they are complete. Labeled transition systems can be distinguished by a wide range of behavioral equivalences [17, 18]. In ... |

194 |
Bisimulation can’t be traced
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...o explore the boundaries for transition rules that constitute sensible semantic definitions. For strong bisimulation equivalence [28], Groote [23] defined the ntyft format (extending the earlier GSOS =-=[9]-=- and tyft [24] formats), which incorporates negative premises. Bol and Groote [10] proved that if a TSS is complete and in the ntyft format, then the strong bisimulation relation induced by its least ... |

189 |
Structured operational semantics and bisimulation as a congruence
- Groote, Vaandrager
- 1992
(Show Context)
Citation Context ... boundaries for transition rules that constitute sensible semantic definitions. For strong bisimulation equivalence [28], Groote [23] defined the ntyft format (extending the earlier GSOS [9] and tyft =-=[24]-=- formats), which incorporates negative premises. Bol and Groote [10] proved that if a TSS is complete and in the ntyft format, then the strong bisimulation relation induced by its least three-valued s... |

135 | The well-founded semantics coincides with the threevalued stable semantics
- Przymusinski
- 1990
(Show Context)
Citation Context ... rule, under a certain substitution, implies validity of the conclusion of this rule under the same substitution. This article focuses on a single-sorted first-order signature for terms. Przymusinski =-=[32]-=- introduced three-valued stable models in order to give meaning to TSSs that incorporate negative premises. Such a model partitions the set of transitions into three disjoint sets: transitions are tru... |

115 |
Transition system specifications with negative premises
- Groote
- 1993
(Show Context)
Citation Context ...[10]) if all transitions in its least three-valued stable model are either true or false. Although in general it is not effectively decidable whether a TSS is complete, the notion of a stratification =-=[23, 31]-=- provides a convenient method to decide for many TSSs in the literature that they are complete. Labeled transition systems can be distinguished by a wide range of behavioral equivalences [17, 18]. In ... |

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 ...rong bisimulation relation induced by its least three-valued stable model is a congruence. (They needed a well-foundedness requirement, which was later shown to be redundant [12].) Baeten and Verhoef =-=[4, 38]-=- extended the tyft and ntyft formats with predicates, to obtain the path and panth formats, respectively. Bloom [8] and Ulidowski [34, 35] introduced congruence formats for branching bisimulation equi... |

78 |
J.I.Zucker: Processes and the Denotational Semantics of Concurrency
- Bakker
- 1982
(Show Context)
Citation Context ...tends an earlier format by Bloom with standard notions such as recursion, iteration, predicates, and negative premises. 1 Introduction Structural operational semantics [29] and denotational semantics =-=[6]-=- have evolved as the two standard methodologies to provide specification languages, programming languages, and process algebras with a semantics. In structural operational semantics, transitions betwe... |

74 |
Syntax and defining equations for an interrupt mechanism in process algebra
- Baeten, Bergstra, et al.
(Show Context)
Citation Context ... paper. We give several examples of operators from the literature that are RBB safe but not RBB cool: recursion [16], iteration [25], empty process [39], and a weaker version of the priority operator =-=[1]-=-. Section 3.4 contains counter-examples to show that the syntactic requirements of the RBB safe format are all essential. Finally, Section 3.5 presents the proof of the congruence theorem. In [11] a p... |

74 |
The meaning of negative premises in transition system specifications
- Bol, Groote
- 1996
(Show Context)
Citation Context ...n limbo is maximal; this so-called least three-valued stable model coincides with the well-founded semantics of van Gelder, Ross, and Schlipf [14]. A TSS is complete [21] (or positive after reduction =-=[10]-=-) if all transitions in its least three-valued stable model are either true or false. Although in general it is not effectively decidable whether a TSS is complete, the notion of a stratification [23,... |

54 | Ntyft/ntyxt rules reduce to ntree rules
- Fokkink, Glabbeek
- 1996
(Show Context)
Citation Context ... ntyft format, then the strong bisimulation relation induced by its least three-valued stable model is a congruence. (They needed a well-foundedness requirement, which was later shown to be redundant =-=[12]-=-.) Baeten and Verhoef [4, 38] extended the tyft and ntyft formats with predicates, to obtain the path and panth formats, respectively. Bloom [8] and Ulidowski [34, 35] introduced congruence formats fo... |

43 |
Structural operational semantics for weak bisimulations
- Bloom
- 1995
(Show Context)
Citation Context ...ess requirement, which was later shown to be redundant [12].) Baeten and Verhoef [4, 38] extended the tyft and ntyft formats with predicates, to obtain the path and panth formats, respectively. Bloom =-=[8]-=- and Ulidowski [34, 35] introduced congruence formats for branching bisimulation equivalence. However, the transition rules for several standard operators in process algebra (most notably alternative ... |

39 | On the relationship between process algebra and input/output automata
- Vaandrager
- 1991
(Show Context)
Citation Context ...nce theorem. In [11] a precongruence format was presented for language preorder, which uses a wild labeling of arguments of function symbols in a similar fashion as in the RBB safe format. Vaandrager =-=[37]-=- introduced precongruence formats for failures, external trace, external failure, and must preorders. van Glabbeek [19] presented congruence formats for ready simulation, ready trace, and failure equi... |

38 | R.: The meaning of negative premises in transition system specifications II
- Glabbeek
- 2004
(Show Context)
Citation Context ... in which the set of transitions in limbo is maximal; this so-called least three-valued stable model coincides with the well-founded semantics of van Gelder, Ross, and Schlipf [14]. A TSS is complete =-=[21]-=- (or positive after reduction [10]) if all transitions in its least three-valued stable model are either true or false. Although in general it is not effectively decidable whether a TSS is complete, t... |

37 | and W.P.Weijland. Process Algebra. Cambridge Tracts in Theoretical Computer Science 18 - Baeten - 1990 |

36 |
Concurrency and automata on in nite sequences
- Park
- 1981
(Show Context)
Citation Context ...f behavioural equivalences, to avoid repetitive congruence proofs, and to explore the boundaries for transition rules that constitute sensible semantic de nitions. For strong bisimulation equivalence =-=[28]-=-, Groote [23] de ned the ntyft format (extending the earlier GSOS [9] and tyft [24] formats), which incorporates negative premises. Bol and Groote [10] proved that if a collection of transition rules ... |

33 | Branching bisimilarity is an equivalence indeed
- Basten
- 1996
(Show Context)
Citation Context ...2 T (\Sigma) are branching bisimilar with respect to C, denoted by s $ b t, if there exists a branching bisimulation relation B such that s B t. Branching bisimulation is an equivalence relation; see =-=[6]-=-. Definition 2.12 An equivalence relation R on T (\Sigma) is called a congruence if s i R t i for i = 1; : : : ; ar (f) implies f(s 1 ; : : : ; s ar(f) ) R f(t 1 ; : : : ; t ar(f) ). Branching bisimul... |

31 | A conservative look at operational semantics with variable binding
- Fokkink, Verhoef
- 1998
(Show Context)
Citation Context ...nd C ff j= N . - For limit ordinals ff we define C ff = [ fi!ff C fi and U ff = " fi!ff U fi . The following two inclusions can be derived for ordinals ff and fi with fisff, by ordinal induction =-=(cf. [13]-=-): 1. C fi ` C ff ; 2. U fi ' U ff . Owing to these two inclusions, the Knaster-Tarski theorem [33] yields that there exists an ordinalssuch that Cs= C +1 and Us= U +1 . It is easy to see that hCs; Us... |

31 |
Bounded nondeterminism and the approximation induction principle in process algebra
- Glabbeek
- 1987
(Show Context)
Citation Context ...rovide answers to three open questions that were posed by Bloom in the conclusion of his paper. We give several examples of operators from the literature that are RBB safe but not RBB cool: recursion =-=[16]-=-, iteration [25], empty process [39], and a weaker version of the priority operator [1]. Section 3.4 contains counter-examples to show that the syntactic requirements of the RBB safe format are all es... |

30 |
Term-rewriting systems with rule priorities. Theoretical Computer Science, 67(2/3):283{301
- Baeten, Bergstra, et al.
- 1989
(Show Context)
Citation Context ...[21]. Stratifications In general it is not effectively decidable whether a finite TSS is complete. Van de Pol [30, Ex. 22] presented a striking example, in the realm of term rewriting with priorities =-=[2]-=-, that it may take more than ! steps to compute the least three-valued stable model for a finite priority rewrite system. In practice, a useful tool for showing that a TSS is complete is the notion of... |

26 |
Representation of events in nerve nets and nite automata, in: C.E
- Kleene
- 1956
(Show Context)
Citation Context ...of the open question that were posed by Bloom in the conclusion of his paper. We give several examples of operators from the 2literature that are RBB safe but not RBB cool: recursion [16], iteration =-=[25]-=-, empty process [35], and a weaker version of the priority operator [1]. Section 3.4 contains counter-examples to show that the syntactic requirements of the RBB safe format are all essential. Finally... |

25 |
A modal characterisation of observable machine-behaviour
- Milner
- 1981
(Show Context)
Citation Context ...alences Supported by a grant from The Nuffield Foundation 1 have been developed to abstract away from internal machine behavior, represented by a silent steps: observation [27], branching [22], delay =-=[26]-=-, and j [3]. This article focuses on branching bisimulation equivalence, in which one can abstract away from an actionsif its execution does not implicate the loss of possible behavior. In recent year... |

25 |
The algebra of communicating processes with empty process
- Vrancken
- 1997
(Show Context)
Citation Context ...ns that were posed by Bloom in the conclusion of his paper. We give several examples of operators from the literature that are RBB safe but not RBB cool: recursion [16], iteration [25], empty process =-=[39]-=-, and a weaker version of the priority operator [1]. Section 3.4 contains counter-examples to show that the syntactic requirements of the RBB safe format are all essential. Finally, Section 3.5 presen... |

22 |
Another look at abstraction in process algebra
- Baeten, Glabbeek
- 1987
(Show Context)
Citation Context ...orted by a grant from The Nuffield Foundation 1 have been developed to abstract away from internal machine behavior, represented by a silent steps: observation [27], branching [22], delay [26], and j =-=[3]-=-. This article focuses on branching bisimulation equivalence, in which one can abstract away from an actionsif its execution does not implicate the loss of possible behavior. In recent years, this equ... |

19 | Full abstraction in structural operational semantics
- Glabbeek
- 1993
(Show Context)
Citation Context ...s of function symbols in a similar fashion as in the RBB safe format. Vaandrager [37] introduced precongruence formats for failures, external trace, external failure, and must preorders. van Glabbeek =-=[19]-=- presented congruence formats for ready simulation, ready trace, and failure equivalence (of which the last two formats are flawed). Bloom [7] formulated a congruence format for trace equivalence. The... |

19 | Equivalences on observable processes
- Ulidowski
- 1992
(Show Context)
Citation Context ...hich was later shown to be redundant [12].) Baeten and Verhoef [4, 38] extended the tyft and ntyft formats with predicates, to obtain the path and panth formats, respectively. Bloom [8] and Ulidowski =-=[34, 35]-=- introduced congruence formats for branching bisimulation equivalence. However, the transition rules for several standard operators in process algebra (most notably alternative composition) are outsid... |

12 |
Syntax and de ning equations for an interrupt mechanism in process algebra
- Baeten, Bergstra, et al.
- 1986
(Show Context)
Citation Context ...aper. We give several examples of operators from the 2literature that are RBB safe but not RBB cool: recursion [16], iteration [25], empty process [35], and a weaker version of the priority operator =-=[1]-=-. Section 3.4 contains counter-examples to show that the syntactic requirements of the RBB safe format are all essential. Finally, Section 3.5 presents the proof of the congruence theorem. Fokkink [11... |

9 | Structural operational semantics for weak bisimulations, Theoret - Bloom - 1995 |

9 |
Transition system speci cations with negative premises
- Groote
- 1993
(Show Context)
Citation Context ... equivalences, to avoid repetitive congruence proofs, and to explore the boundaries for transition rules that constitute sensible semantic de nitions. For strong bisimulation equivalence [28], Groote =-=[23]-=- de ned the ntyft format (extending the earlier GSOS [9] and tyft [24] formats), which incorporates negative premises. Bol and Groote [10] proved that if a collection of transition rules is complete a... |

8 | Algebraic Techniques for Concurrency and their Application - Vaandrager - 1990 |

7 | Formats of ordered SOS rules with silent actions
- Ulidowski, Phillips
- 1997
(Show Context)
Citation Context ...hich was later shown to be redundant [12].) Baeten and Verhoef [4, 38] extended the tyft and ntyft formats with predicates, to obtain the path and panth formats, respectively. Bloom [8] and Ulidowski =-=[34, 35]-=- introduced congruence formats for branching bisimulation equivalence. However, the transition rules for several standard operators in process algebra (most notably alternative composition) are outsid... |

6 | de Pol. Operational semantics of rewriting with priorities - van - 1998 |

5 |
When is partial trace equivalence adequate
- Bloom
- 1994
(Show Context)
Citation Context ...race, external failure, and must preorders. van Glabbeek [19] presented congruence formats for ready simulation, ready trace, and failure equivalence (of which the last two formats are flawed). Bloom =-=[7]-=- formulated a congruence format for trace equivalence. The expressivity of the RBB safe format is incomparable with each of those formats. 2 Preliminaries 2.1 Terms Definition 2.1 A signature \Sigma c... |

4 | Language preorder as a precongruence
- Fokkink
(Show Context)
Citation Context ...ator [1]. Section 3.4 contains counter-examples to show that the syntactic requirements of the RBB safe format are all essential. Finally, Section 3.5 presents the proof of the congruence theorem. In =-=[11]-=- a precongruence format was presented for language preorder, which uses a wild labeling of arguments of function symbols in a similar fashion as in the RBB safe format. Vaandrager [37] introduced prec... |

4 |
What is branching time and why to use it
- Glabbeek
- 1994
(Show Context)
Citation Context ...act away from an actionsif its execution does not implicate the loss of possible behavior. In recent years, this equivalence has been used in a sizable number of verifications in process algebra. See =-=[20]-=- for a lucid exposition on the motivations behind the definition of branching bisimulation equivalence. In general, a behavioral equivalence relation induced by a TSS is not a congruence; that is, the... |

2 | Klop, Syntax and defining equations for an interrupt mechanism in process algebra, Fund - Baeten, Bergstra, et al. - 1996 |

2 |
A lattice theoretical xed point theorem and its applications. Paci c
- Tarski
- 1955
(Show Context)
Citation Context ...0 = ;, and C \ F = ;. The following two inclusions can be derived for ordinals and with , by ordinal induction (c.f. [13]): 1. C C ; 2. F F . Owing to these two inclusions, the Knaster-Tarski theorem =-=[31]-=- yields that there exists an ordinal such that C = C +1 and F = F +1. It is easy to see that hC ; F i is a three-valued stable model for T (owing to the de nitions of 2 C +1 and 62 F +1). Furthermore,... |

1 | Language preorder as a precongruence, Theoret - Fokkink |