## Ntyft/ntyxt rules reduce to ntree rules (1996)

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Venue: | Information and Computation |

Citations: | 54 - 18 self |

### BibTeX

@ARTICLE{Fokkink96ntyft/ntyxtrules,

author = {Wan Fokkink and Rob Van Glabbeek},

title = {Ntyft/ntyxt rules reduce to ntree rules},

journal = {Information and Computation},

year = {1996},

volume = {126},

pages = {1--10}

}

### Years of Citing Articles

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### Abstract

Groote and Vaandrager introduced the tyft/tyxt format for Transition System Specifications (TSSs), and established that for each TSS in this format that is well-founded, the bisimulation equivalence it induces is a congruence. In this paper, we construct for each TSS in tyft/tyxt format an equivalent TSS that consists of tree rules only. As a corollary we can give an affirmative answer to an open question, namely whether the well-foundedness condition in the congruence theorem for tyft/tyxt can be dropped. These results extend to tyft/tyxt with negative premises and predicates. 1

### Citations

1500 | The Stable Model Semantics For Logic Programming
- Gelfond, Lifschitz
- 1988
(Show Context)
Citation Context ...rules such as t t a −→/ a −→ t ′ One of the most general ways to associate transitions to TSSs with negative premises is through the notion of stability, which was introduced by Gelfond and Lifschitz =-=[8]-=- in logic programming. The transition relation determined by a TSS is then its unique stable transition relation if such exists. Bol and Groote [4], who adapted this notion for TSSs, showed that there... |

1288 | A Structural Approach to Operational Semantics
- Plotkin
- 1981
(Show Context)
Citation Context ... the congruence theorem for tyft/tyxt can be dropped. These results extend to tyft/tyxt with negative premises and predicates. 1 Introduction Structural operational semantics, as advocated by Plotkin =-=[15]-=-, is currently a popular method to provide process algebras and specification languages with an interpretation. It is based on the use of transition systems. Given a set of states, the transitions bet... |

847 | The Well-Founded Semantics for General Logic Programs
- Gelder, Ross, et al.
- 1991
(Show Context)
Citation Context ... not a congruence. However, they found a subclass of such TSSs for which it is. They defined a (somewhat complicated) notion of reduction of TSSs, inspired by the work of Van Gelder, Ross and Schlipf =-=[7]-=- in logic programming, and proved a congruence theorem for well-founded TSSs in the ntyft/ntyxt format that are positive (that is without negative premises) after applying reduction. The transition re... |

657 |
Concurrency and Automata on Infinite Sequences
- Park
- 1981
(Show Context)
Citation Context ...hin the scope of this format. To distinguish such labelled transition systems, many different equivalences have been defined, one of the finest of which is the strong bisimulation equivalence of Park =-=[14]-=-. In general, this equivalence is not a congruence, i.e. the equivalence class of a term f(p1, ..., pm) modulo strong bisimulation is not always determined by the equivalence classes of the terms pi. ... |

417 |
Logic Programming
- Apt
- 1990
(Show Context)
Citation Context ...tween terms is unifiable, then there exists a unifier ρ ′ for E such that each unifier for E is also a unifier for ρ ′ . This result follows from the well-known Martelli-Montanari algorithm [13]. See =-=[1]-=- for the basic definitions and for an introduction to the field of logic programming and unification. In Fokkink [6], this theorem is generalized to the case where E may be infinite. The first propert... |

334 | An Efficient Unification Algorithm
- Martelli, Montanari
- 1982
(Show Context)
Citation Context ...uations between terms is unifiable, then there exists a unifier ρ ′ for E such that each unifier for E is also a unifier for ρ ′ . This result follows from the well-known Martelli-Montanari algorithm =-=[13]-=-. See [1] for the basic definitions and for an introduction to the field of logic programming and unification. In Fokkink [6], this theorem is generalized to the case where E may be infinite. The firs... |

194 |
Bisimulation can’t be traced
- Bloom, Istrail, et al.
- 1995
(Show Context)
Citation Context ...which ensure that the bisimulation equivalence induced by a TSS in such a format is always a congruence. A first proposal was made by De Simone [16], which was generalized by Bloom, Istrail and Meyer =-=[3]-=- to the GSOS format. Next, Groote and Vaandrager [12] introduced the tyft/tyxt format, and proved a congruence theorem for TSSs in this format that satisfy a well-foundedness criterion. Up to now, it ... |

189 |
Structured operational semantics and bisimulation as a congruence
- Groote, Vaandrager
- 1992
(Show Context)
Citation Context ...ed by a TSS in such a format is always a congruence. A first proposal was made by De Simone [16], which was generalized by Bloom, Istrail and Meyer [3] to the GSOS format. Next, Groote and Vaandrager =-=[12]-=- introduced the tyft/tyxt format, and proved a congruence theorem for TSSs in this format that satisfy a well-foundedness criterion. Up to now, it has been an open question whether or not well-founded... |

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

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 ...s such that • if c ∈ H then H/c ∈ R ⊢ , and • if K/c ∈ R and H/σ(d) ∈ R ⊢ for all d ∈ K and some substitution σ, then H/σ(c) ∈ R ⊢ . For notions of provability found elsewhere in the literature (e.g. =-=[2, 4, 5, 9, 10, 11, 12, 17]-=-) the following proposition is easily obtained. By establishing the same for our notion, it follows that it coincides with the others. The proposition only holds for small TSSs, but this restriction w... |

74 |
The meaning of negative premises in transition system specifications
- Bol, Groote
- 1996
(Show Context)
Citation Context ...s such that • if c ∈ H then H/c ∈ R ⊢ , and • if K/c ∈ R and H/σ(d) ∈ R ⊢ for all d ∈ K and some substitution σ, then H/σ(c) ∈ R ⊢ . For notions of provability found elsewhere in the literature (e.g. =-=[2, 4, 5, 9, 10, 11, 12, 17]-=-) the following proposition is easily obtained. By establishing the same for our notion, it follows that it coincides with the others. The proposition only holds for small TSSs, but this restriction w... |

63 | Higher-level synchronising devices in Meije-SCCS - Simone - 1985 |

54 | Bisimulation can’t be traced: Preliminary report
- Bloom, Istrail, et al.
- 1988
(Show Context)
Citation Context ...which ensure that the bisimulation equivalence induced by a TSS in such a format is always a congruence. A first proposal was made by De Simone [16], which was generalized by Bloom, Istrail and Meyer =-=[3]-=- to the GSOS format. Next, Groote and Vaandrager [12] introduced the tyft/tyxt format, and proved a congruence theorem for TSSs in this format that satisfy a well-foundedness criterion. Current affili... |

38 | R.: The meaning of negative premises in transition system specifications II
- Glabbeek
- 2004
(Show Context)
Citation Context ...s such that • if c ∈ H then H/c ∈ R ⊢ , and • if K/c ∈ R and H/σ(d) ∈ R ⊢ for all d ∈ K and some substitution σ, then H/σ(c) ∈ R ⊢ . For notions of provability found elsewhere in the literature (e.g. =-=[2, 4, 5, 9, 10, 11, 12, 17]-=-) the following proposition is easily obtained. By establishing the same for our notion, it follows that it coincides with the others. The proposition only holds for small TSSs, but this restriction w... |

35 |
Higher-level synchronising devices
- Simone
- 1985
(Show Context)
Citation Context ...xiomatic framework. Several formats have been developed which ensure that the bisimulation equivalence induced by a TSS in such a format is always a congruence. A first proposal was made by De Simone =-=[16]-=-, which was generalized by Bloom, Istrail and Meyer [3] to the GSOS format. Next, Groote and Vaandrager [12] introduced the tyft/tyxt format, and proved a congruence theorem for TSSs in this format th... |

25 | Logic Programming"; Handbook of Theoretical Computer Science - Apt - 1990 |

19 | Full abstraction in structural operational semantics
- Glabbeek
- 1993
(Show Context)
Citation Context ...ience of applying this theorem, since the user no longer has to recall and check the complicated well-foundedness criterion. The main result of this paper was obtained independently by the authors in =-=[9]-=- and [5]. Our present proof improves the ones envisioned in [9] and given in [5]. It makes heavy use of a standard result from unification theory, which says that for each set of equations that is uni... |

16 | The tyft/tyxt format reduces to tree rules
- Fokkink
- 1994
(Show Context)
Citation Context ... applying this theorem, since the user no longer has to recall and check the complicated well-foundedness criterion. The main result of this paper was obtained independently by the authors in [9] and =-=[5]-=-. Our present proof improves the ones envisioned in [9] and given in [5]. It makes heavy use of a standard result from unification theory, which says that for each set of equations that is unifiable, ... |

1 |
Idempotent Most General Unifiers for Infinite Sets,'' Report CS-R9442
- Fokkink
- 1994
(Show Context)
Citation Context ...ns that have a finite domain. However, we will need the result in a setting which does not satisfy these finiteness constraints. A proof of the unification result in the infinite case can be found in =-=[6]-=-. Here we prove the special case of this result that is needed for our main theorem. Groote [11] added negative premises to tyft/tyxt, resulting in the ntyft/ntyxt format (that also generalizes the GS... |