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## On the Minimisation of Acyclic Models ⋆

Citations: | 1 - 0 self |

### Citations

3885 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...weak bisimilarity is the largest strong, respectively weak bisimulation [16]. For an IMC 〈S, s 0 ,A,Ri, ∅〉 the above definitions reduce to Milner’s standard definitions on labelled transition systems =-=[21]-=-. 3 Strong Bisimulation for Acyclic IMCs To decide strong bisimulation on unlabelled acyclic digraphs, a linear-time algorithm has been developed in [9], which is based on state ranking. To handle lab... |

976 |
Matrix multiplication via arithmetic progressions
- Coppersmith, Winograd
- 1990
(Show Context)
Citation Context ... to compute the transitive closure of internal transitions. This directly determines the overall complexity to be O(n 3 ) (disregarding some very specialized algorithms for transitive closure such as =-=[6]-=-). As first noted in [15], the transitive closure computation does not dominate in practical applications, and then the complexity is O(m ∗ log n), where m ∗ is the number of transitions after closure... |

546 | An introduction to Input/Output automata
- Lynch, MR
- 1989
(Show Context)
Citation Context ...arkov chains. In compositional dynamic fault tree (DFT) analysis [4] the components of a DFT are modelled using IOIMCs. The IOIMC formalism is a variant of the IMC formalism, inspired by I/O automata =-=[19]-=-, in which the actions of a model are divided into input, output and internal transitions. The difference between weak Markovian bisimulation for IMCs and for IOIMCs is that for IOIMCs there may be mo... |

444 |
Tarjan, Three partition refinement algorithms
- Paige, E
- 1987
(Show Context)
Citation Context ...ustrial settings [7, 18]. The algorithmic problem to minimise a labelled transition system with respect to bisimulation is well studied. For strong bisimulation, a partition refinement based approach =-=[22]-=- can be used to achieve an algorithm with complexity O(m log n), where m and n denote the number of transitions and states of the model. The computation of weak and branching bisimulation is theoretic... |

114 |
Interactive Markov Chains: The Quest for Quantified Quality
- Hermanns
- 2002
(Show Context)
Citation Context ...regation techniques [3, 17]. They are used to model and study ‘quantified uncertainty” in many areas, such as embedded, networked, randomized, and biological systems. Interactive Markov chains (IMCs) =-=[16]-=- constitute a process algebraic formalism to construct such models. Recently, an extension of IMCs with input and output (IOIMCs) [4] has been introduced to define a rigorous compositional semantics f... |

95 | CADP 2006: A toolbox for the construction and analysis of distributed processes
- Garavel
- 2007
(Show Context)
Citation Context ...ion, composition and minimisation steps are intertwined along the structure of the compositional specification. This strategy is central to explicit-state verification tools such as μCRL [1] and CADP =-=[12]-=-, and arguably a central backbone of their successes in industrial settings [7, 18]. The algorithmic problem to minimise a labelled transition system with respect to bisimulation is well studied. For ... |

80 | Boyd.: Dynamic fault-tree models for fault-tolerant computer systems - Dugan, Bavuso, et al. - 1992 |

70 | An efficient algorithm for branching bisimulation and stuttering equivalence
- Groote, Vaandrager
- 1990
(Show Context)
Citation Context ...ve closure of internal transitions. This directly determines the overall complexity to be O(n 3 ) (disregarding some very specialized algorithms for transitive closure such as [6]). As first noted in =-=[15]-=-, the transitive closure computation does not dominate in practical applications, and then the complexity is O(m ∗ log n), where m ∗ is the number of transitions after closure. ⋆ This work is supporte... |

47 |
An improved algorithm for transitive closure on acyclic digraphs. TCS
- Simon
- 1988
(Show Context)
Citation Context ...y not the case in practice, as also noted in [15]. In the general case the best theoretical complexity for computing the reflexive transitive closure is O(n2.376 ) as given by [6]. For acyclic graphs =-=[23]-=- gives an algorithm which computes the reflexive transitive closure in time O(mk) where k is the size of the chain decomposition of the model (which is at most n). In our implementation we have adapte... |

43 | A fast bisimulation algorithm
- Dovier, Piazza, et al.
(Show Context)
Citation Context ...]. Wimmer et al. [25] have taken up this idea to arrive at a fully symbolic implementation of the signature-refinement approach, to effectively bridge to BDD-based representations of state spaces. In =-=[9]-=-, an algorithm with O(m) complexity has been proposed for deciding strong bisimulation on directed acyclic graphs. Mateescu [20] developed an O(m) algorithm for checking modal mu calculus on acyclic L... |

37 | Bisimulation minimisation mostly speeds up probabilistic
- Kemna, Zapreev, et al.
(Show Context)
Citation Context ...checking weak bisimulation, then requiring O(m 2 ). Stochastic behavioural models are among the most prominent application areas for bisimulation minimisation and compositional aggregation techniques =-=[3, 17]-=-. They are used to model and study ‘quantified uncertainty” in many areas, such as embedded, networked, randomized, and biological systems. Interactive Markov chains (IMCs) [16] constitute a process a... |

17 | Revisiting interactive markov chains - Bravetti - 2002 |

15 |
Distributed branching bisimulation reduction of state spaces
- Blom, Orzan
(Show Context)
Citation Context ...tion problem has triggered work in at least three different directions. Orzan and Blom have devised an efficient distributed algorithm for bisimulation minimisation, based on the notion of signatures =-=[2]-=-. Wimmer et al. [25] have taken up this idea to arrive at a fully symbolic implementation of the signature-refinement approach, to effectively bridge to BDD-based representations of state spaces. In [... |

14 |
A reduct-and-closure algorithm for graphs
- Goralciková, Koubek
- 1979
(Show Context)
Citation Context ...computes the reflexive transitive closure in time O(mk) where k is the size of the chain decomposition of the model (which is at most n). In our implementation we have adapted the simple algorithm in =-=[13]-=- which has worstcase time complexity O(mn). Theoretically the algorithm is then still cubic in the number of states, but we will discuss why this is often not the case in practice. For acyclic models ... |

13 |
B.: Compositional performability evaluation for Statemate
- Böde, Herbstritt, et al.
- 2006
(Show Context)
Citation Context ...checking weak bisimulation, then requiring O(m 2 ). Stochastic behavioural models are among the most prominent application areas for bisimulation minimisation and compositional aggregation techniques =-=[3, 17]-=-. They are used to model and study ‘quantified uncertainty” in many areas, such as embedded, networked, randomized, and biological systems. Interactive Markov chains (IMCs) [16] constitute a process a... |

13 | Local model-checking of modal mu-calculus on acyclic labeled transition systems
- Mateescu
- 2002
(Show Context)
Citation Context ..., to effectively bridge to BDD-based representations of state spaces. In [9], an algorithm with O(m) complexity has been proposed for deciding strong bisimulation on directed acyclic graphs. Mateescu =-=[20]-=- developed an O(m) algorithm for checking modal mu calculus on acyclic LTS, which can be instantiated to checking weak bisimulation, then requiring O(m 2 ). Stochastic behavioural models are among the... |

13 | Sigrefa symbolic bisimulation tool box
- Wimmer, Herbstritt, et al.
- 2006
(Show Context)
Citation Context ...iggered work in at least three different directions. Orzan and Blom have devised an efficient distributed algorithm for bisimulation minimisation, based on the notion of signatures [2]. Wimmer et al. =-=[25]-=- have taken up this idea to arrive at a fully symbolic implementation of the signature-refinement approach, to effectively bridge to BDD-based representations of state spaces. In [9], an algorithm wit... |

11 |
Refined Interfaces for Compositional Verification
- Lang
- 2006
(Show Context)
Citation Context ...he compositional specification. This strategy is central to explicit-state verification tools such as μCRL [1] and CADP [12], and arguably a central backbone of their successes in industrial settings =-=[7, 18]-=-. The algorithmic problem to minimise a labelled transition system with respect to bisimulation is well studied. For strong bisimulation, a partition refinement based approach [22] can be used to achi... |

6 | A theory of normed simulations - Griffioen, Vaandrager |

4 | M.: Quantitative evaluation in embedded system design: Validation of multiprocessor multithreaded architectures
- Coste, Garavel, et al.
- 2008
(Show Context)
Citation Context ...he compositional specification. This strategy is central to explicit-state verification tools such as μCRL [1] and CADP [12], and arguably a central backbone of their successes in industrial settings =-=[7, 18]-=-. The algorithmic problem to minimise a labelled transition system with respect to bisimulation is well studied. For strong bisimulation, a partition refinement based approach [22] can be used to achi... |

2 |
A compositional semantics for dynamic fault trees in input/output interactive markov chains
- Boudali, Crouzen, et al.
- 2007
(Show Context)
Citation Context ...domized, and biological systems. Interactive Markov chains (IMCs) [16] constitute a process algebraic formalism to construct such models. Recently, an extension of IMCs with input and output (IOIMCs) =-=[4]-=- has been introduced to define a rigorous compositional semantics for dynamic fault trees (DFTs). Fault trees and DFTs are in daily use in industrial dependability engineering [10, 24]. The analysis o... |

2 | Cones and foci: A mechanical framework for protocol verification - Fokkink, Pang, et al. - 2006 |

1 |
L.: No Cycling? Go Faster! On the minimization of acyclic models
- Crouzen, Hermanns, et al.
(Show Context)
Citation Context ...sions which allow us to handle the models appearing in DFT analysis. Section 6 presents experimental results after we which we conclude. Detailed proofs for the theorems in this paper can be found in =-=[8]-=-.On the Minimisation of Acyclic Models 297 2 Preliminaries In this section we introduce the definition of acyclic interactive Markov chains, strong and weak bisimulations [16]. Definition 1. An inter... |

1 |
D.: Fault Tree Handbook. NASA
- Vesely, Goldberg, et al.
- 1981
(Show Context)
Citation Context ... and output (IOIMCs) [4] has been introduced to define a rigorous compositional semantics for dynamic fault trees (DFTs). Fault trees and DFTs are in daily use in industrial dependability engineering =-=[10, 24]-=-. The analysis of DFTs via their IOIMC semantics relies heavily on compositional aggregation and weak bisimulation minimisation [4]. Remarkably, the IOIMC semantics maps on acyclic structures. This is... |