## Language preorder as a precongruence

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Venue: | Theoretical Computer Science |

Citations: | 4 - 4 self |

### BibTeX

@ARTICLE{Fokkink_languagepreorder,

author = {Wan Fokkink},

title = {Language preorder as a precongruence},

journal = {Theoretical Computer Science},

year = {},

volume = {243},

pages = {200--0}

}

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### Abstract

Groote and Vaandrager introduced the tyft format, which is a congruence format for strong bisimulation equivalence. This article proposes additional syntactic requirements on the tyft format, extended with predicates, to obtain a precongruence format for language preorder. 1

### Citations

1418 |
A Calculus of Communicating Systems
- Milner
- 1980
(Show Context)
Citation Context ...2: Transition Rules for the Binary Kleene Star Corollary 4.1 Language preorder is a precongruence with respect to BPA . 4.2 Communication Let A represent a collection of atomic actions. The merge skt =-=[18]-=- executes its two arguments in parallel. If s or t can execute an action a, then skt can also execute 14a. Moreover, there is a communication function : A A ! A, and if s and t can execute actions a ... |

1371 | A structural approach to operational semantics
- Plotkin
- 1981
(Show Context)
Citation Context ..., extended with predicates, to obtain a precongruence format for language preorder. Keywords: language preorder, precongruence, tyft format, predicates 1 Introduction Structural operational semantics =-=[20]-=- is a popular method to provide formal languages, process algebras, and speci cation languages with an interpretation. It is based on the use of transition systems. Given a set of states, the transiti... |

699 | Concurrency and automata on infinite sequences - Park - 1981 |

394 | Representation of Events in Nerve Nets and Finite Automata - Kleene - 1956 |

384 | Process algebra for synchronous communication
- Bergstra, Klop
- 1984
(Show Context)
Citation Context ...3.2]. We show as an example that the transition rules for regular expressions are L cool, so that the congruence property follows automatically. Furthermore, we show that the transition rules for ACP =-=[5]-=- and for recursion [11] are L cool. In contrast with positive premises, negative premises of a transition rule have to be invalid in order to imply the conclusion of the rule, under a certain substitu... |

310 | The linear time – branching time spectrum II (The semantics of sequential systems with silent moves
- Glabbeek
- 1993
(Show Context)
Citation Context ...e closed terms generated by a single-sorted rst-order signature, and transitions are supplied with labels. Labelled transition systems can be distinguished by a wide range of behavioural equivalences =-=[12]-=-, one of the coarsest of which is language equivalence. Two processes are language equivalent if they can terminate successfully with exactly the same sequences of actions. Language equivalence underl... |

293 |
Regular Algebra and Finite Machines
- Conway
- 1971
(Show Context)
Citation Context ... equivalent if they can terminate successfully with exactly the same sequences of actions. Language equivalence underlies the algebra of regular expressions initiated by Kleene [16]; see for instance =-=[10, 8]-=-. In general, the language equivalence induced by a TSS is not a congruence, i.e., the equivalence class of a term f(p1; :::; pn) need not be determined by the equivalence classes of its arguments p1;... |

201 |
Structured operational semantics and bisimulation as a congruence
- Groote, Vaandrager
- 1992
(Show Context)
Citation Context ...nce formats have been developed for a number of behavioural equivalences, rstly to avoid repetitive congruence proofs, secondly to explore the limits of sensible TSS de nitions. Groote and Vaandrager =-=[15]-=- introduced a congruence format for bisimulation equivalence called tyft/tyxt, supplied with a well-foundedness criterion. Sponsored in part by a grant from The Nu eld Foundation. 1Fokkink and van Gl... |

200 | A completeness theorem for Kleene algebras and the algebra of regular events
- Kozen
- 1994
(Show Context)
Citation Context ...on, sequential composition, and the Kleene star. The axiomatizability of regular expressions modulo language equivalence has been investigated in several articles. For example, Salomaa [21] and Kozen =-=[17]-=- presented complete axiomatizations. The fact that its operators preserve language equivalence is folklore; see for example [21, Theo. 1] and [1, Prop. 3.2]. We show as an example that the transition ... |

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

114 | A congruence theorem for structured operational semantics with predicates
- Baeten, Verhoef
- 1993
(Show Context)
Citation Context ...th a well-foundedness criterion. Sponsored in part by a grant from The Nu eld Foundation. 1Fokkink and van Glabbeek [9] showed that this well-foundedness criterion can be omitted. Baeten and Verhoef =-=[3]-=- extended tyft/tyxt with predicates, to obtain the path format. This article introduces a syntactic format for TSSs, and it is shown that the language equivalence induced by a TSS in this format is al... |

83 |
Two complete axiom systems for the algebra of regular events
- Salomaa
- 1966
(Show Context)
Citation Context ...ative composition, sequential composition, and the Kleene star. The axiomatizability of regular expressions modulo language equivalence has been investigated in several articles. For example, Salomaa =-=[21]-=- and Kozen [17] presented complete axiomatizations. The fact that its operators preserve language equivalence is folklore; see for example [21, Theo. 1] and [1, Prop. 3.2]. We show as an example that ... |

76 | Syntax and defining equations for an interrupt mechanism in process algebra - Baeten, Bergstra, et al. |

74 | The meaning of negative premises in transition system specifications
- Bol, Groote
- 1996
(Show Context)
Citation Context ...ansition rule have to be invalid in order to imply the conclusion of the rule, under a certain substitution. The path format for bisimulation equivalence has been extended with negative premises; see =-=[14, 22, 7]-=-. However, negative premises do not combine well with language equivalence. For instance, the transition rules for the priority operator [2], which include negative premises, do not preserve language ... |

54 | Ntyft/ntyxt rules reduce to ntree rules
- Fokkink, Glabbeek
- 1996
(Show Context)
Citation Context ...uced a congruence format for bisimulation equivalence called tyft/tyxt, supplied with a well-foundedness criterion. Sponsored in part by a grant from The Nu eld Foundation. 1Fokkink and van Glabbeek =-=[9]-=- showed that this well-foundedness criterion can be omitted. Baeten and Verhoef [3] extended tyft/tyxt with predicates, to obtain the path format. This article introduces a syntactic format for TSSs, ... |

52 |
Algebraic theory of automata
- Ginzburg
- 1968
(Show Context)
Citation Context ... equivalent if they can terminate successfully with exactly the same sequences of actions. Language equivalence underlies the algebra of regular expressions initiated by Kleene [16]; see for instance =-=[10, 8]-=-. In general, the language equivalence induced by a TSS is not a congruence, i.e., the equivalence class of a term f(p1; :::; pn) need not be determined by the equivalence classes of its arguments p1;... |

44 |
Structural operational semantics for weak bisimulations
- Bloom
- 1995
(Show Context)
Citation Context ...priority operator [2], which include negative premises, do not preserve language equivalence. We show that a general congruence format for language equivalence cannot include negative premises. Bloom =-=[6]-=- suggested congruence formats RBB cool and RWB cool for rooted branching and weak equivalence, respectively. Van Glabbeek [13] sketched congruence formats for ready simulation, ready trace, failure tr... |

36 |
Concurrency and automata on in nite sequences
- Park
- 1981
(Show Context)
Citation Context ...t ti ' L si for i = 1; :::; ar(f) implies f(t1; :::; t ar (f )) ' L f(s1; :::; s ar (f )). 2.4 Path Rules Groote and Vaandrager [15] introduced a congruence format for strong bisimulation equivalence =-=[19]-=-, called the tyft/tyxt format. We follow the approach of Baeten and Verhoef [3], who extended the tyft/tyxt format with predicates such as a ! p , to obtain the path format. We present the de nition o... |

32 |
Bounded nondeterminism and the approximation induction pri ciple in process algebra
- Glabbeek
- 1987
(Show Context)
Citation Context ...ample that the transition rules for regular expressions are L cool, so that the congruence property follows automatically. Furthermore, we show that the transition rules for ACP [5] and for recursion =-=[11]-=- are L cool. In contrast with positive premises, negative premises of a transition rule have to be invalid in order to imply the conclusion of the rule, under a certain substitution. The path format f... |

27 |
Representation of events in nerve nets and nite automata
- Kleene
- 1956
(Show Context)
Citation Context ... processes are language equivalent if they can terminate successfully with exactly the same sequences of actions. Language equivalence underlies the algebra of regular expressions initiated by Kleene =-=[16]-=-; see for instance [10, 8]. In general, the language equivalence induced by a TSS is not a congruence, i.e., the equivalence class of a term f(p1; :::; pn) need not be determined by the equivalence cl... |

24 | A menagerie of non-finitely based process semantics over BPA*—from ready simulation to completed traces - Aceto, Fokkink, et al. - 1998 |

19 | Full abstraction in structural operational semantics
- Glabbeek
- 1993
(Show Context)
Citation Context ...ce format for language equivalence cannot include negative premises. Bloom [6] suggested congruence formats RBB cool and RWB cool for rooted branching and weak equivalence, respectively. Van Glabbeek =-=[13]-=- sketched congruence formats for ready simulation, ready trace, failure trace, and trace equivalence. The L cool format is incomparable with each of these formats. 2 Preliminaries 2.1 Signature De nit... |

12 |
Syntax and de ning equations for an interrupt mechanism in process algebra
- Baeten, Bergstra, et al.
- 1986
(Show Context)
Citation Context ...lence has been extended with negative premises; see [14, 22, 7]. However, negative premises do not combine well with language equivalence. For instance, the transition rules for the priority operator =-=[2]-=-, which include negative premises, do not preserve language equivalence. We show that a general congruence format for language equivalence cannot include negative premises. Bloom [6] suggested congrue... |

9 |
Transition system speci cations with negative premises
- Groote
- 1993
(Show Context)
Citation Context ...ansition rule have to be invalid in order to imply the conclusion of the rule, under a certain substitution. The path format for bisimulation equivalence has been extended with negative premises; see =-=[14, 22, 7]-=-. However, negative premises do not combine well with language equivalence. For instance, the transition rules for the priority operator [2], which include negative premises, do not preserve language ... |

3 | A menagerie of non- nitely based process semantics over - Aceto, Fokkink, et al. |