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## General quantitative specification theories with modalities (2012)

Venue: | Juhani Karhumäki, Arto Lepistö, and Michail Prilutskii, editors, CSR, volume 7353 of LNCS |

Citations: | 5 - 4 self |

### Citations

354 |
Infinite Dimensional Analysis: a Hitchhiker’s Guide. 2nd edition
- Aliprantis, Border
- 1999
(Show Context)
Citation Context ...). Hence also this distance is asymmetric; the intuition is that any label in JkK has to be matched as good as possible inJ`K. Note the similarity of this to the construction of Hausdorff metric; cf. =-=[20, 1]-=- for background material on hemimetrics and the Hausdorff construction. We will assume given an abstract trace distance dT : Spec ∞ × Spec∞ → L which has a recursive expression using a distance iterat... |

116 |
Positional strategies for mean payoff games,
- Ehrenfeucht, Mycielski
- 1979
(Show Context)
Citation Context ...τ) = ∑ j λ jd(σj , τj) for implementation traces of equal length. This distance hence accumulates individual distances on labels; it has been studied for weighted transition systems and games e.g. in =-=[5, 7, 8, 19, 23, 25, 26]-=-. [2] develops a complete specification theory around this specific distance; we will continue this example below to show how it fits in our present context. Example 2. With the same instantiations of... |

78 | Abstraction-based model checking using modal transition systems. - Godefroid, Huth, et al. - 2001 |

64 | Quantitative languages, in
- Chatterjee, Doyen, et al.
(Show Context)
Citation Context ...ey are unable to quantify the impact of small variations. For quantifying differences, distances between systems are useful; this approach has been 2 Bauer, Fahrenberg, Legay, Thrane explored e.g. in =-=[5, 7, 19, 23, 25]-=-. A first quantitative specification theory which is not fragile is introduced in [2], for one specific type of weighted modal transition systems and one specific distance. While this is useful for so... |

43 | Modeling and Model Checking Software Product Lines. - Gruler, Leucker, et al. - 2008 |

34 | Timed I/O Automata: A Complete Specification Theory for Real-time Systems.
- David, Larsen, et al.
- 2010
(Show Context)
Citation Context ...he usual discrete label set of transition systems, permitting to reason about quantitative aspects of models and specifications. These quantitative labels can be used to model and analyze e.g. timing =-=[6, 16]-=-, resource usage [22], or energy consumption [4, 9]. In particular, [17] extends modal transition systems with integer intervals and introduces corresponding extensions of the above operations which o... |

24 |
Modal specifications. In Automatic Verification Methods for Finite State Systems,
- Larsen
- 1989
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Citation Context ...theorem shows that the modal refinement distance overapproximates the thorough one, and that it is exact for deterministic SMTS. This is similar to the situation for standard modal transition systems =-=[18]-=-; note [18] that deterministic specifications generally suffice for applications. Theorem 1. For all SMTS S, T , dt(S, T ) vL dm(S, T ). If T is deterministic, then dt(S, T ) = dm(S, T ). In a quantit... |

20 | Quantifying similarities between timed systems
- Henzinger, Majumdar, et al.
- 2005
(Show Context)
Citation Context ...he usual discrete label set of transition systems, permitting to reason about quantitative aspects of models and specifications. These quantitative labels can be used to model and analyze e.g. timing =-=[6, 16]-=-, resource usage [22], or energy consumption [4, 9]. In particular, [17] extends modal transition systems with integer intervals and introduces corresponding extensions of the above operations which o... |

19 |
A Behavioural Pseudometric for Metric Labelled Transition Systems.
- Breugel
- 2005
(Show Context)
Citation Context ...ey are unable to quantify the impact of small variations. For quantifying differences, distances between systems are useful; this approach has been 2 Bauer, Fahrenberg, Legay, Thrane explored e.g. in =-=[5, 7, 19, 23, 25]-=-. A first quantitative specification theory which is not fragile is introduced in [2], for one specific type of weighted modal transition systems and one specific distance. While this is useful for so... |

17 | Don’t know in the µ-calculus. - Grumberg, Lange, et al. - 2005 |

16 |
Quantitative analysis of real-time systems using priced timed automata,”
- Bouyer, Fahrenberg, et al.
- 2012
(Show Context)
Citation Context ...ermitting to reason about quantitative aspects of models and specifications. These quantitative labels can be used to model and analyze e.g. timing [6, 16], resource usage [22], or energy consumption =-=[4, 9]-=-. In particular, [17] extends modal transition systems with integer intervals and introduces corresponding extensions of the above operations which observe the added quantitative information, and [3] ... |

14 | Linear and branching system metrics
- Alfaro, Faella, et al.
- 2009
(Show Context)
Citation Context ...ey are unable to quantify the impact of small variations. For quantifying differences, distances between systems are useful; this approach has been 2 Bauer, Fahrenberg, Legay, Thrane explored e.g. in =-=[5, 7, 19, 23, 25]-=-. A first quantitative specification theory which is not fragile is introduced in [2], for one specific type of weighted modal transition systems and one specific distance. While this is useful for so... |

13 | Modal Transition Systems as the Basis for Interface Theories and Product Lines. - Nyman - 2008 |

12 | Energy Games in Multiweighted Automata
- Fahrenberg, Juhl, et al.
- 2011
(Show Context)
Citation Context ...ermitting to reason about quantitative aspects of models and specifications. These quantitative labels can be used to model and analyze e.g. timing [6, 16], resource usage [22], or energy consumption =-=[4, 9]-=-. In particular, [17] extends modal transition systems with integer intervals and introduces corresponding extensions of the above operations which observe the added quantitative information, and [3] ... |

8 |
On using priced timed automata to achieve optimal scheduling
- Rasmussen, Larsen, et al.
- 2006
(Show Context)
Citation Context ...set of transition systems, permitting to reason about quantitative aspects of models and specifications. These quantitative labels can be used to model and analyze e.g. timing [6, 16], resource usage =-=[22]-=-, or energy consumption [4, 9]. In particular, [17] extends modal transition systems with integer intervals and introduces corresponding extensions of the above operations which observe the added quan... |

6 | Quantitative refinement for weighted modal transition systems
- Bauer, Fahrenberg, et al.
- 2011
(Show Context)
Citation Context ...ween systems are useful; this approach has been 2 Bauer, Fahrenberg, Legay, Thrane explored e.g. in [5, 7, 19, 23, 25]. A first quantitative specification theory which is not fragile is introduced in =-=[2]-=-, for one specific type of weighted modal transition systems and one specific distance. While this is useful for some applications, it is too specific to cover the whole spectrum of quantitative speci... |

6 |
Extending modal transition systems with structured labels
- Bauer, Juhl, et al.
(Show Context)
Citation Context ... that allows to decide whether an implementation is a model of the specification, (2) a notion of refinement for determining the relationship between specifications and their sets of implementations, =-=(3)-=- a structural composition which, at the abstract level, mimics the behavioral composition of systems, (4) a quotient that allows to synthesize specifications from refinements, and (5) a logical compos... |

6 | The quantitative linear-time–branchingtime spectrum
- Fahrenberg, Legay, et al.
- 2011
(Show Context)
Citation Context ...tion theory that is independent of both the specific labels and the distance used to measure differences; this is what we introduce in this paper. Using the concept of distance iterator function from =-=[10, 12]-=-, we introduce a general notion of refinement distance between structured modal transition systems and a general quantitative specification theory. It turns out that there are some natural technical c... |

6 | The complexity of mean payoff games
- Zwick, Paterson
- 1995
(Show Context)
Citation Context ...τ) = ∑ j λ jd(σj , τj) for implementation traces of equal length. This distance hence accumulates individual distances on labels; it has been studied for weighted transition systems and games e.g. in =-=[5, 7, 8, 19, 23, 25, 26]-=-. [2] develops a complete specification theory around this specific distance; we will continue this example below to show how it fits in our present context. Example 2. With the same instantiations of... |

5 |
Distances for weighted transition systems: Games and properties
- Fahrenberg, Thrane, et al.
(Show Context)
Citation Context ...tion theory that is independent of both the specific labels and the distance used to measure differences; this is what we introduce in this paper. Using the concept of distance iterator function from =-=[10, 12]-=-, we introduce a general notion of refinement distance between structured modal transition systems and a general quantitative specification theory. It turns out that there are some natural technical c... |

5 |
Quantitative simulations of weighted transition systems
- Thrane, Fahrenberg, et al.
(Show Context)
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5 | A theory of metric labelled transition systems
- Breugel
- 1996
(Show Context)
Citation Context ...f −→S = 99KS ⊆ S× Imp×S; hence in an implementation, all optional behavior has been resolved, and all data has been refined to implementation labels. We will assume all SMTS to be compactly branching =-=[24]-=-, that is, for any SMTS S and any s ∈ S, the sets {k ∈ Spec | s k99K s′} and {k ∈ Spec | s k−→ s′} are to be compact under the label metric d. This is a common assumption in quantitative formalisms wh... |

3 |
Modal transition systems with weight intervals
- Juhl, Larsen, et al.
- 2011
(Show Context)
Citation Context ...8, 21], which are labeled transition systems equipped with two types of transitions: must transitions that are mandatory for any implementation, and may transitions which are optional. In recent work =-=[3, 17]-=-, modal transition systems have been extended by adding richer information to the usual discrete label set of transition systems, permitting to reason about quantitative aspects of models and specific... |

3 |
Metrics for weighted transition systems: Axiomatization and complexity
- Larsen, Fahrenberg, et al.
(Show Context)
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1 |
Make a difference! (Semantically
- Fahrenberg, Legay, et al.
- 2011
(Show Context)
Citation Context ...in standard conditions, quotient is sound and maximal with respect to ‖. Note that the property that X ≤m TsS General Quantitative Specification Theories 9 iff S‖X ≤m T implies uniqueness of quotient =-=[11]-=-; hence if a certain instantiation of our framework admits a quotient which is not quantitatively well-behaved, there is no hope that one can find another one which is. Theorem 3. Let S, T , X be SMTS... |