#### DMCA

## LTL model checking of time-inhomogeneous Markov chains (2009)

Venue: | in Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis |

Citations: | 4 - 1 self |

### Citations

370 | A Logic for Reasoning about Time and Reliability
- Hansson, Jonsson
- 1994
(Show Context)
Citation Context ...]. Temporal logics and accompanying model-checking algorithms have been developed for discrete-time Markov chains (DTMCs for short), against linear-time properties [8,9] and branching-time properties =-=[11]-=-; for CTMCs against branching-time properties [2,3] and linear real-time properties [6]. And some of them have resulted in a number of successful model checkers such as PRISM [12] and MRMC [14]. Howev... |

282 | PRISM: A tool for automatic verification of probabilistic systems. Tools and Algorithms for the Construction and Analysis of Systems
- Hinton, Kwiatkowska, et al.
- 2006
(Show Context)
Citation Context ...hing-time properties [11]; for CTMCs against branching-time properties [2,3] and linear real-time properties [6]. And some of them have resulted in a number of successful model checkers such as PRISM =-=[12]-=- and MRMC [14]. However, the verification of time-inhomogeneous CTMCs (ICTMCs) has – to the best of our knowledge – not yet been investigated in depth, with the notable exception [15], which considere... |

250 |
Numerical methods for ordinary differential systems: the initial value problem
- Lambert
- 1991
(Show Context)
Citation Context ...bsorbing (and thus obtaining C[F ]) followed by solving a system of homogeneous ODEs (7) for C[F ]. By using standard numerical approaches, e.g., Euler method or Runge-Kutta method and their variants =-=[16]-=-, this system of ODEs (i.e. the transient probability vector) can be solved. 3.2 Time-Unbounded Reachability We then turn to the time-unbounded reachability problem, i.e., there are no constraints on ... |

235 | Model-checking algorithms for continuous-time markov chains.
- Baier, Haverkort, et al.
- 2003
(Show Context)
Citation Context ... algorithms have been developed for discrete-time Markov chains (DTMCs for short), against linear-time properties [8,9] and branching-time properties [11]; for CTMCs against branching-time properties =-=[2,3]-=- and linear real-time properties [6]. And some of them have resulted in a number of successful model checkers such as PRISM [12] and MRMC [14]. However, the verification of time-inhomogeneous CTMCs (I... |

215 |
M.: The complexity of probabilistic verification
- Courcoubetis, Yannakakis
- 1995
(Show Context)
Citation Context ...tions, are much more appropriate [17]. Temporal logics and accompanying model-checking algorithms have been developed for discrete-time Markov chains (DTMCs for short), against linear-time properties =-=[8,9]-=- and branching-time properties [11]; for CTMCs against branching-time properties [2,3] and linear real-time properties [6]. And some of them have resulted in a number of successful model checkers such... |

96 |
J.-P.: Principles of Model Checking
- Baier, Katoen
- 2008
(Show Context)
Citation Context ...teps (since the time-unbounded case is considered), i.e., ProbDC[F ](s,♦ atF ). This can be done by standard methods, e.g., value iteration or solving a system of linear equations, see, among others, =-=[4]-=- (Ch. 10). Theorem 2. Let C = (S, AP, L, α,R(t)) be an ICTMC satisfying EPA with time TEP and PEP, s ∈ S and F ⊆ S. Then: ProbCEP(s, 0,♦ atF )= ∑ s′∈S ProbC[F ](s, 0,♦=TEPats′)·ProbDC[F ](s′,♦ atF ) (... |

68 | A Markov reward model checker.
- Katoen, Khattri, et al.
- 2002
(Show Context)
Citation Context ...erties [11]; for CTMCs against branching-time properties [2,3] and linear real-time properties [6]. And some of them have resulted in a number of successful model checkers such as PRISM [12] and MRMC =-=[14]-=-. However, the verification of time-inhomogeneous CTMCs (ICTMCs) has – to the best of our knowledge – not yet been investigated in depth, with the notable exception [15], which considered model checki... |

23 | Mereacre, Model checking of continuoustime Markov chains against timed automata specifications
- Chen, Han, et al.
(Show Context)
Citation Context ...screte-time Markov chains (DTMCs for short), against linear-time properties [8,9] and branching-time properties [11]; for CTMCs against branching-time properties [2,3] and linear real-time properties =-=[6]-=-. And some of them have resulted in a number of successful model checkers such as PRISM [12] and MRMC [14]. However, the verification of time-inhomogeneous CTMCs (ICTMCs) has – to the best of our know... |

20 |
Model-checking continous-time Markov chains
- Aziz, Sanwal, et al.
(Show Context)
Citation Context ... algorithms have been developed for discrete-time Markov chains (DTMCs for short), against linear-time properties [8,9] and branching-time properties [11]; for CTMCs against branching-time properties =-=[2,3]-=- and linear real-time properties [6]. And some of them have resulted in a number of successful model checkers such as PRISM [12] and MRMC [14]. However, the verification of time-inhomogeneous CTMCs (I... |

18 | An optimal automata approach to LTL model checking of probabilistic systems
- Couvreur, Saheb, et al.
- 2003
(Show Context)
Citation Context ...tions, are much more appropriate [17]. Temporal logics and accompanying model-checking algorithms have been developed for discrete-time Markov chains (DTMCs for short), against linear-time properties =-=[8,9]-=- and branching-time properties [11]; for CTMCs against branching-time properties [2,3] and linear real-time properties [6]. And some of them have resulted in a number of successful model checkers such... |

17 |
Complementation, disambiguation, and determinization of büchi automata unified
- Kähler, Wilke
- 2008
(Show Context)
Citation Context ... crucial for the remainder of this paper. A closely related notion, referred to as unambiguous, has been widely studied in automata and language theory, dating back to [1]. See also, among others, [5]=-=[13]-=- for relevant literature. To the best of our knowledge, the notion of “separated” was firstly exploited in [9] for model checking DTMCs against LTL. Definition 7 (Product). Given an ICTMC C = (S, AP, ... |

11 | Computing battery lifetime distributions
- Cloth, Haverkort, et al.
- 2007
(Show Context)
Citation Context ...some situations constant rates do not adequately model real behaviors. This applies, e.g., to failure rates of hardware components [10] (that usually depend on the component’s age), battery depletion =-=[7]-=- (where the power extraction rate non-linearly depends on the remaining amount of energy), and random phenomena that are subject to environmental influences. In these circumstances, Markov models Fi... |

9 |
2003): Unambiguous Büchi automata
- Carton, Michel
(Show Context)
Citation Context ... is crucial for the remainder of this paper. A closely related notion, referred to as unambiguous, has been widely studied in automata and language theory, dating back to [1]. See also, among others, =-=[5]-=-[13] for relevant literature. To the best of our knowledge, the notion of “separated” was firstly exploited in [9] for model checking DTMCs against LTL. Definition 7 (Product). Given an ICTMC C = (S, ... |

8 |
Exact methods for the transient analysis of nonhomogeneous continuous time Markov chains
- Rindos, Woolet, et al.
- 1995
(Show Context)
Citation Context .... c© Springer-Verlag Berlin Heidelberg 2009 LTL Model Checking of Time-Inhomogeneous Markov Chains 105 with inhomogeneous rates, i.e., rates that are time-varying functions, are much more appropriate =-=[17]-=-. Temporal logics and accompanying model-checking algorithms have been developed for discrete-time Markov chains (DTMCs for short), against linear-time properties [8,9] and branching-time properties [... |

6 | Analysis of software fault removal policies using a non-homogeneous continuous time Markov chain.
- Gokhale, Lyu, et al.
- 2004
(Show Context)
Citation Context ...e probabilistic nature of mode transitions are constant. However, in some situations constant rates do not adequately model real behaviors. This applies, e.g., to failure rates of hardware components =-=[10]-=- (that usually depend on the component’s age), battery depletion [7] (where the power extraction rate non-linearly depends on the remaining amount of energy), and random phenomena that are subject to ... |

4 |
Model checking hml on piecewise-constant inhomogeneous Markov chains
- Katoen, Mereacre
(Show Context)
Citation Context ...rs such as PRISM [12] and MRMC [14]. However, the verification of time-inhomogeneous CTMCs (ICTMCs) has – to the best of our knowledge – not yet been investigated in depth, with the notable exception =-=[15]-=-, which considered model checking a simple stochastic variant of Hennessy-Milner Logic (without fixed points) for piecewise-constant ICTMCs. The main aim of the current paper is to fill this gap by co... |

3 |
Rational omega-languages are non-ambiguous
- Arnold
- 1983
(Show Context)
Citation Context ...t of LTL formulae) satisfying: (ρ, t) |= tt (ρ, t) |= ϕ1 ∧ ϕ2 iff (ρ, t) |= ϕ1 and (ρ, t) |= ϕ2 (ρ, t) |= a iff a ∈ L(ρ@t) (ρ, t) |= ¬ϕ iff (ρ, t) |= ϕ (ρ, t) |= X ϕ iff ∃Δt 0. (ρ, t+Δt) |= ϕ and ρ=-=[1]-=- = ρ@(t+Δt) (ρ, t) |= ϕ1 U ϕ2 iff ∃Δt 0. (ρ, t+Δt) |= ϕ2 and ∀t′ < t+Δt. (ρ, t′) |= ϕ1 We use ats∈AP as an atomic proposition which holds solely at state s. For F ⊆ S, we write atF for ∨ s∈F ats. Le... |