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## Partial order reduction for probabilistic systems (2004)

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### Other Repositories/Bibliography

Venue: | In Proc. 1st QEST |

Citations: | 30 - 3 self |

### Citations

1623 |
The Temporal Logic of Programs
- Pnueli
- 1977
(Show Context)
Citation Context .... with the help of process equivalences and model checking against temporal logical specifications. In the context of specifiying probabilistic systems against formulas of Linear Temporal Logic (LTL) =-=[39]-=- a specification consists of a LTL-formula ϕ that expresses a certain path property and a probability bound, e.g. “= 1”, “≥ p”or “< p” for some p ∈ [0,1]. Hence, LTL can serve to formulate qualitative... |

690 |
An automata-theoretic approach to automatic program verification
- Vardi, Wolper
- 1986
(Show Context)
Citation Context ... explore the state space and algorithms that construct an automaton for the given formula) and their combination with numerical methods to solve linear equation systems or linear programming problems =-=[45, 46, 9, 40, 10, 13, 11, 6]-=-. Thus, the state-explosion problem is as least as relevant (or even more) than in the non-probabilistic setting. To reason about non-probabilistic systems, a variety of methods have been developed to... |

521 | Bisimulation through probabilistic testing
- Larsen, Skou
- 1991
(Show Context)
Citation Context ... an MDP, any state s might have several outgoing actionlabeled transitions, each of them is associated with a proba2 bility distribution which yields the probabilities for the successor states. As in =-=[41, 33, 13]-=- we assume here that for any state s, the outgoing transitions of s have different action labels. (This corresponds to the so-called reactive model in the classification of [44].) In addition, we assu... |

310 |
Automatic verification of probabilistic concurrent finite-state programs
- Vardi
- 1985
(Show Context)
Citation Context ... explore the state space and algorithms that construct an automaton for the given formula) and their combination with numerical methods to solve linear equation systems or linear programming problems =-=[45, 46, 9, 40, 10, 13, 11, 6]-=-. Thus, the state-explosion problem is as least as relevant (or even more) than in the non-probabilistic setting. To reason about non-probabilistic systems, a variety of methods have been developed to... |

288 |
A stubborn attack on state explosion
- Valmari
- 1991
(Show Context)
Citation Context ...ular, the original and reduced MDP are fully equivalent for LTL \X specifications. We followed here the approach of the ample sets, but we expect that also the concepts of persistent [18] or stubborn =-=[43, 42]-=- sets could be adapted for the probabilistic case. Compared to the non-probabilistic case, we needed an auxiliary condition (A5) which requires singleton ample sets to avoid probabilistic branches in ... |

231 | PRISM: Probabilistic symbolic model checker
- Kwiatkowska, Norman, et al.
- 2001
(Show Context)
Citation Context ...on methods that combat the state-explosion problem has mainly concentrated on symbolic techniques with variants of decision diagrams [20, 2, 5, 22, 34, 31]. For instance, the PCTLmodel checkers PRISM =-=[30]-=-, ProbVERUS [21] and RAPTURE [28] are based on a symbolic representation of the system by a multiterminal BDD. Beside the symbolic DDbased methods there is a variety of results about the stateaggregat... |

217 |
Specifying concurrent program modules
- Lamport
- 1983
(Show Context)
Citation Context ... in a MDP are called stutter equivalent iff the induced words trace(ς1) and trace(ς2) over 2 AP are stutter equivalent. It is well-known that stutter equivalent paths fulfill the same LTL \X formulas =-=[32]-=-. For the partial order reduction we shall need the concept of stutter actions, i.e., actions that have no effect on the statelabels, no matter in which state they are taken. Formally, action α of a M... |

201 | Probabilistic Symbolic Model Checking with PRISM: A Hybrid Approach
- Kwiatkowska, Norman, et al.
- 2002
(Show Context)
Citation Context ...e e.g. [8] for an overview. In the probabilistic setting, research on methods that combat the state-explosion problem has mainly concentrated on symbolic techniques with variants of decision diagrams =-=[20, 2, 5, 22, 34, 31]-=-. For instance, the PCTLmodel checkers PRISM [30], ProbVERUS [21] and RAPTURE [28] are based on a symbolic representation of the system by a multiterminal BDD. Beside the symbolic DDbased methods ther... |

193 | Reactive, generative, and stratified models of probabilistic processes
- Glabbeek, Smolka, et al.
- 1995
(Show Context)
Citation Context ... states. As in [41, 33, 13] we assume here that for any state s, the outgoing transitions of s have different action labels. (This corresponds to the so-called reactive model in the classification of =-=[44]-=-.) In addition, we assume here a labelling function that attaches to any state s a set of atomic propositions that are assumed to hold in state s. The atomic propositions will serve as atoms to formul... |

183 | All from one, one for all: on model checking using representatives
- Peled
- 1993
(Show Context)
Citation Context ...ter equivalence classes of paths agree. Although this leads to some technical difficulties in the correctness proof, we show in this paper that with only slight modifications Peled’s ample set method =-=[35]-=- can be adapted for the probabilistic setting and the verification of LTL \X properties (or even stutter insensitive ωregular properties). Compared to Peled’s approach, we need an additional condition... |

123 | An Improvement in Formal Verification
- Holzmann, Peled
- 1994
(Show Context)
Citation Context ...stem by a representation of the subsystems that run in parallel, e.g., as in the (non-probabilistic) model checker SPIN [23]. The rough idea behind partial order reduction in nonprobabilistic systems =-=[24, 42, 18, 19, 37]-=- is to construct a reduced state graph by abolishing redundancies in the transition system that origin from the interleaving of independent activities that are executed in parallel. For independent ac... |

111 |
Markov Decision Processes—Discrete Stochastic Dynamic Programming
- Puterman
- 1994
(Show Context)
Citation Context ... an MDP, any state s might have several outgoing actionlabeled transitions, each of them is associated with a proba2 bility distribution which yields the probabilities for the successor states. As in =-=[41, 33, 13]-=- we assume here that for any state s, the outgoing transitions of s have different action labels. (This corresponds to the so-called reactive model in the classification of [44].) In addition, we assu... |

59 | Weak bisimulation for probabilistic systems
- Philippou, Lee, et al.
- 2000
(Show Context)
Citation Context ...esentation of the system by a multiterminal BDD. Beside the symbolic DDbased methods there is a variety of results about the stateaggregation with (formula-independent) bisimulation-like equivalences =-=[27, 3, 38, 7]-=- and property-driven abstraction techniques [12, 25, 26]. As far as we know this paper is the first that investigates partial order reduction for probabilistic systems. The starting point is a descrip... |

47 |
Probabilistic Verification
- Pnueli, Zuck
- 1993
(Show Context)
Citation Context ... explore the state space and algorithms that construct an automaton for the given formula) and their combination with numerical methods to solve linear equation systems or linear programming problems =-=[45, 46, 9, 40, 10, 13, 11, 6]-=-. Thus, the state-explosion problem is as least as relevant (or even more) than in the non-probabilistic setting. To reason about non-probabilistic systems, a variety of methods have been developed to... |

43 | Static partial order reduction
- Kurshan, Levin, et al.
- 1998
(Show Context)
Citation Context ...perties [16, 36] as these cover our auxiliary condition. A possibly better reduction can be achieved by reformulating the algorithms for non-probabilistic systems and linear time properties (see e.g. =-=[36, 8, 29]-=-) in such a way that the auxiliary condition is taken into account. Organization of the paper. Section 2 briefly summarizes the preliminaries concerning our model (Markov decision processes). The ampl... |

39 |
Partial order reduction: Linear and branching temporal logics and process algebras
- Peled
- 1996
(Show Context)
Citation Context ...robabilistic systems can also be used for the probabilistic setting. One possibility is to use exactly the same techniques as they are known for nonprobabilistic systems and branching-time properties =-=[16, 36]-=- as these cover our auxiliary condition. A possibly better reduction can be achieved by reformulating the algorithms for non-probabilistic systems and linear time properties (see e.g. [36, 8, 29]) in ... |

28 | Rapture: A tool for verifying Markov decision processes
- Jeannet, dArgenio, et al.
(Show Context)
Citation Context ...explosion problem has mainly concentrated on symbolic techniques with variants of decision diagrams [20, 2, 5, 22, 34, 31]. For instance, the PCTLmodel checkers PRISM [30], ProbVERUS [21] and RAPTURE =-=[28]-=- are based on a symbolic representation of the system by a multiterminal BDD. Beside the symbolic DDbased methods there is a variety of results about the stateaggregation with (formula-independent) bi... |

18 |
On some equivalence relations for probabilistic processes
- Huynh, Tian
- 1992
(Show Context)
Citation Context ...esentation of the system by a multiterminal BDD. Beside the symbolic DDbased methods there is a variety of results about the stateaggregation with (formula-independent) bisimulation-like equivalences =-=[27, 3, 38, 7]-=- and property-driven abstraction techniques [12, 25, 26]. As far as we know this paper is the first that investigates partial order reduction for probabilistic systems. The starting point is a descrip... |

18 | Symbolic Representations and Analysis of Large Probabilistic Systems
- Miner, Parker
- 2004
(Show Context)
Citation Context ...e e.g. [8] for an overview. In the probabilistic setting, research on methods that combat the state-explosion problem has mainly concentrated on symbolic techniques with variants of decision diagrams =-=[20, 2, 5, 22, 34, 31]-=-. For instance, the PCTLmodel checkers PRISM [30], ProbVERUS [21] and RAPTURE [28] are based on a symbolic representation of the system by a multiterminal BDD. Beside the symbolic DDbased methods ther... |

11 |
State of the Art Report: Stubborn Sets
- Valmari
- 1994
(Show Context)
Citation Context ...stem by a representation of the subsystems that run in parallel, e.g., as in the (non-probabilistic) model checker SPIN [23]. The rough idea behind partial order reduction in nonprobabilistic systems =-=[24, 42, 18, 19, 37]-=- is to construct a reduced state graph by abolishing redundancies in the transition system that origin from the interleaving of independent activities that are executed in parallel. For independent ac... |

5 | 2002b) Possibilistic and Probabilistic Abstraction-Based Model Checking
- Huth
(Show Context)
Citation Context ...e symbolic DDbased methods there is a variety of results about the stateaggregation with (formula-independent) bisimulation-like equivalences [27, 3, 38, 7] and property-driven abstraction techniques =-=[12, 25, 26]-=-. As far as we know this paper is the first that investigates partial order reduction for probabilistic systems. The starting point is a description of an asynchronous parallel system by a representat... |

5 |
Abstraction and probabilities for hybrid logics
- Huth
- 2005
(Show Context)
Citation Context ...e symbolic DDbased methods there is a variety of results about the stateaggregation with (formula-independent) bisimulation-like equivalences [27, 3, 38, 7] and property-driven abstraction techniques =-=[12, 25, 26]-=-. As far as we know this paper is the first that investigates partial order reduction for probabilistic systems. The starting point is a description of an asynchronous parallel system by a representat... |