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## 2007): Bisimulation Minimisation Mostly Speeds Up Probabilistic Model Checking

Venue: | In: Tools and Algorithms for the Construction and Analysis of Systems, 13th International Conference (TACAS’07), Lecture Notes in Computer Science 4424 |

Citations: | 39 - 9 self |

### Citations

835 | Crowds: Anonymity for web transactions
- Reiter, Rubin
- 1998
(Show Context)
Citation Context ...Hz Pentium 4 processor with 1 GB RAM running Linux. All reported times are in milliseconds and are obtained by taking the average of running the experiment 10 times. 4.1 Discrete time Crowds protocol =-=[38]-=-. This protocol uses random routing within a group of nodes (a crowd) to establish a connection path between a sender and a receiver. Rout4 Up to states s where the set { σ ∈ Path D (s) | σ �|= Φ U Ψ ... |

757 | A Compositional Approach to Performance Modelling
- Hillston
- 1994
(Show Context)
Citation Context ...Probabilistic model checking engines have been integrated in existing tool chains for widely used formalisms such as stochastic Petri nets [11], Statemate [9], and the stochastic process algebra PEPA =-=[24]-=-, and are used for a probabilistic extension of Promela [4]. The typical kind of properties that can be checked is time-bounded reachability properties—“Does the probability to reach a certain set of ... |

526 | Bisimulation through probabilistic testing
- Larsen, Skou
- 1991
(Show Context)
Citation Context ...focus on fully probabilistic models such as discrete-time and continuous-time Markov chains (DTMCs and CTMCs, for short), and variants thereof with costs. The advantages of probabilistic bisimulation =-=[34]-=- in this setting are manifold. It preserves the validity of PCTL [20] and CSL [2, 6] formulas, variants of CTL for the discrete- and continuous-time probabilistic setting, respectively. It implies ord... |

235 | Model-checking algorithms for continuous-time markov chains.
- Baier, Haverkort, et al.
- 2003
(Show Context)
Citation Context ...ov chains (DTMCs and CTMCs, for short), and variants thereof with costs. The advantages of probabilistic bisimulation [34] in this setting are manifold. It preserves the validity of PCTL [20] and CSL =-=[2, 6]-=- formulas, variants of CTL for the discrete- and continuous-time probabilistic setting, respectively. It implies ordinary lumpability of Markov chains [10], an aggregation technique for Markov chains ... |

205 | Probabilistic symbolic model checking with PRISM: A hybrid approach
- Kwiatkowska, Norman, et al.
- 2004
(Show Context)
Citation Context ...sions thereof that are tailored to the property to be checked. 1 Introduction Probabilistic model checking enjoys a rapid increase of interest from different communities. Software tools such as PRISM =-=[31]-=- (with about 4,000 downloads), MRMC [29], and LiQuor [4] support the verification of Markov chains or variants thereof that exhibit nondeterminism. They have been applied to case studies from areas su... |

116 | Exact and ordinary lumpability in finite Markov chains.
- Buchholz
- 1994
(Show Context)
Citation Context ...reserves the validity of PCTL [20] and CSL [2, 6] formulas, variants of CTL for the discrete- and continuous-time probabilistic setting, respectively. It implies ordinary lumpability of Markov chains =-=[10]-=-, an aggregation technique for Markov chains that is applied in performance and dependability evaluation since the 1960s. Quotient Markov chains can be obtained in a fully automated way. The time comp... |

102 | It Usually Works: The Temporal Logic of Stochastic Systems
- Aziz, Singhal, et al.
- 1995
(Show Context)
Citation Context ...ion R on D with s1 R s2. F-bisimulation on CTMCs (for a set of CSL formulas F) is defined analogously [5]. Note that strong bisimilarity is Fbisimilarity for F = AP. Preservation results. Aziz et al. =-=[3]-=- have shown that strong bisimulation is sound and complete with respect to PCTL (and even PCTL ∗ ): Proposition 1. Let D be a DTMC, R a bisimulation and s an arbitrary state of D. Then, for all PCTL f... |

93 | Symmetry Breaking in Distributed Networks
- Itai, Rodeh
- 1990
(Show Context)
Citation Context ... 6.6 15 3 19228 55948 102 53 23 0.2 363 4.4 15 4 119800 352260 790 97 190 0.5 1235 4.1 15 5 592060 1754860 4670 153 1020 0.9 3870 4.6 15 6 2464168 7347928 20600 221 4180 1.5 11150 4.9 Leader election =-=[28]-=-. In this protocol, N nodes that are arranged in an unidirectional ring select an identity randomly according to a uniform distribution on { 1, . . .,K }. By means of synchronous message passing, proc... |

91 |
A logic for reasoning about time and reliability. Formal aspects of computing,
- Hansson, Jonsson
- 1994
(Show Context)
Citation Context ...ous-time Markov chains (DTMCs and CTMCs, for short), and variants thereof with costs. The advantages of probabilistic bisimulation [34] in this setting are manifold. It preserves the validity of PCTL =-=[20]-=- and CSL [2, 6] formulas, variants of CTL for the discrete- and continuous-time probabilistic setting, respectively. It implies ordinary lumpability of Markov chains [10], an aggregation technique for... |

82 | Modular model checking. In
- Kupferman, Vardi
- 1997
(Show Context)
Citation Context ...tween bisimulation and MTBDDs would unnecessarily complicate our study; such symbolic representations mostly grow under bisimulation minimisation [23]. Thanks to extensive studies by Fisler and Vardi =-=[16,17,18]-=-, it is known that bisimulation minimisation for LTL model checking and invariant verification leads to drastic state space reductions (up to logarithmic savings) but at a time penalty: the time to mi... |

81 | R.: Model checking Continuous Time Markov Chains
- Aziz, Sanwal, et al.
(Show Context)
Citation Context ...ov chains (DTMCs and CTMCs, for short), and variants thereof with costs. The advantages of probabilistic bisimulation [34] in this setting are manifold. It preserves the validity of PCTL [20] and CSL =-=[2, 6]-=- formulas, variants of CTL for the discrete- and continuous-time probabilistic setting, respectively. It implies ordinary lumpability of Markov chains [10], an aggregation technique for Markov chains ... |

73 | Reachability analysis of probabilistic systems by successive refinements.
- D’Argenio, Jeannet, et al.
- 2001
(Show Context)
Citation Context ...iagrams (multi-terminal BDDs) have been (and still are) successfully applied in PRISM [31] to a range of probabilistic models, abstraction-refinement has been applied to reachability problems in MDPs =-=[12]-=-, partial-order reduction techniques using Peled’s ample-set method have been generalised to MDPs [19], abstract interpretation has been applied to MDPs [36], and various bisimulation equivalences and... |

68 | A Markov reward model checker.
- Katoen, Khattri, et al.
- 2002
(Show Context)
Citation Context ...roperty to be checked. 1 Introduction Probabilistic model checking enjoys a rapid increase of interest from different communities. Software tools such as PRISM [31] (with about 4,000 downloads), MRMC =-=[29]-=-, and LiQuor [4] support the verification of Markov chains or variants thereof that exhibit nondeterminism. They have been applied to case studies from areas such as randomised distributed algorithms,... |

64 | Comparative Branching-Time Semantics for Markov Chains.
- Baier, Katoen, et al.
- 2005
(Show Context)
Citation Context ...eneralised to MDPs [19], abstract interpretation has been applied to MDPs [36], and various bisimulation equivalences and simulation pre-orders allow model aggregation prior to model checking, e. g., =-=[7,39]-=-. Recently proposed techniques include abstractions of probabilities by intervals combined with three-valued logics for DTMCs [15,25,26], stochastic ordering techniques for CSL model checking [8], abs... |

61 |
Stochastic Petri net models of polling systems
- Ibe, Trivedi
- 1990
(Show Context)
Citation Context ... 175 0.01 19662 0.9 5 2 162 193 0.1 12 0.1 0.02 13.5 0.9 5 4 5122 6145 2.8 12 2.9 0.02 427 0.9 5 6 38882 46657 28 12 26 0.02 3240 1.1 5 8 163842 196609 140 12 115 0.02 13653 1.2 Cyclic polling server =-=[27]-=-. This standard example in performance analysis considers a set of stations that are allowed to process a job once they possess the token. The single token circulates among the stations. The times for... |

53 | Game-based abstraction for Markov decision processes.
- Kwiatkowska, Norman, et al.
- 2006
(Show Context)
Citation Context ...ons of probabilities by intervals combined with three-valued logics for DTMCs [15,25,26], stochastic ordering techniques for CSL model checking [8], abstraction of MDPs by two-player stochastic games =-=[32]-=-, and symmetry reduction [33]. The purpose of this paper is to empirically investigate the effect of strong bisimulation minimisation in probabilistic model checking. We hereby focus on fully probabil... |

52 | On the Logical Characterisation of Performability Properties”,
- Baier, Haverkort, et al.
- 2000
(Show Context)
Citation Context ...s underlying CTMC. Let σ = s0 t0 s1 t1 . . . be a path. For t = �k−1 j=0 tj + t ′ with t ′ ≤ tk we define r(σ, t) = �k−1 j=0 tj · r(sj) + t ′ · r(sk), the cumulative reward along σ up to time t. CSRL =-=[5]-=- is a logic that extends CSL with one operator P⊲⊳ p(Φ U ≤t ≤r Ψ) to express time- and reward-bounded properties. Checking this property of a CMRM is difficult. One can either approximate the CMRM by ... |

52 |
Verification of multiprocess probabilistic protocols
- Pnueli, Zuck
- 1986
(Show Context)
Citation Context ...72 17920 62 52 53 4.0 58 15.5 24 2.9 128 17.9 12 73728 577536 3050 3460 103 120 716 25.4 36 55 2048 62.9 15 737280 6881280 39000 32100 151 1590 4883 24.5 45 580 16384 55.3 Randomised mutual exclusion =-=[37]-=-. In this mutual exclusion algorithm, N processes make random choices based on coin tosses to ensure that they can all enter their critical sections eventually, although not simultaneously. The follow... |

44 | Symmetry Reduction for Probabilistic Model Checking
- Kwiatkowska, Norman, et al.
(Show Context)
Citation Context ...vals combined with three-valued logics for DTMCs [15,25,26], stochastic ordering techniques for CSL model checking [8], abstraction of MDPs by two-player stochastic games [32], and symmetry reduction =-=[33]-=-. The purpose of this paper is to empirically investigate the effect of strong bisimulation minimisation in probabilistic model checking. We hereby focus on fully probabilistic models such as discrete... |

36 | Model checking performability properties. In:
- Haverkort, Cloth, et al.
- 2003
(Show Context)
Citation Context ...] which has a time complexity in O(k·r·|S| 3 ), where k and r are the time-bound and reward-bound, respectively. For CMRMs, we employed the discretization approach by Tijms and Veldman as proposed in =-=[21]-=- which runs in time O(t·r·|S| 3 ·d−2 ) where d is the step size of the discretisation. In our experiments, the default setting is d = 1 32 . For the Crowds protocol (for R = 3), we checked the probabi... |

34 | V.: Don’t know in probabilistic systems
- Fecher, Leucker, et al.
- 2006
(Show Context)
Citation Context ... pre-orders allow model aggregation prior to model checking, e. g., [7,39]. Recently proposed techniques include abstractions of probabilities by intervals combined with three-valued logics for DTMCs =-=[15,25,26]-=-, stochastic ordering techniques for CSL model checking [8], abstraction of MDPs by two-player stochastic games [32], and symmetry reduction [33]. The purpose of this paper is to empirically investiga... |

28 | Optimal state-space lumping in Markov chains.
- Derisavi, Hermanns, et al.
- 2003
(Show Context)
Citation Context ...rithmic in the number of states, and linear in the number of transitions—as for traditional bisimulation minimisation— when using splay trees (a specific kind of balanced tree) for storing partitions =-=[14]-=-. Besides, probabilistic bisimulation can be used for obtaining (coarser) abstractions that are tailored to the properties of interest (as we will see), and enjoys the congruence property for parallel... |

27 | Abstract interpretation of programs as Markov decision processes
- Monniaux
- 2005
(Show Context)
Citation Context ...n applied to reachability problems in MDPs [12], partial-order reduction techniques using Peled’s ample-set method have been generalised to MDPs [19], abstract interpretation has been applied to MDPs =-=[36]-=-, and various bisimulation equivalences and simulation pre-orders allow model aggregation prior to model checking, e. g., [7,39]. Recently proposed techniques include abstractions of probabilities by ... |

26 | On the use of MTBDDs for performability analysis and verification of stochastic systems
- Hermanns, Kwiatkowska, et al.
- 2003
(Show Context)
Citation Context ...xplicit model checking as the non-trivial interplay between bisimulation and MTBDDs would unnecessarily complicate our study; such symbolic representations mostly grow under bisimulation minimisation =-=[23]-=-. Thanks to extensive studies by Fisler and Vardi [16–18], it is known that bisimulation minimisation for LTL model checking and invariant verification leads to drastic state space reductions (up to l... |

23 |
On finite-state approximants for probabilistic computation tree logic
- Huth
- 2005
(Show Context)
Citation Context ... pre-orders allow model aggregation prior to model checking, e. g., [7,39]. Recently proposed techniques include abstractions of probabilities by intervals combined with three-valued logics for DTMCs =-=[15,25,26]-=-, stochastic ordering techniques for CSL model checking [8], abstraction of MDPs by two-player stochastic games [32], and symmetry reduction [33]. The purpose of this paper is to empirically investiga... |

19 |
Discrete-time rewards model-checked.
- Andova, Hermanns, et al.
- 2003
(Show Context)
Citation Context ...lts. Section 5 concludes the paper. 2 Preliminaries DTMCs. Let AP be a fixed, finite set of atomic propositions. A (labelled) DTMC D is a tuple (S,P, L) where S is a finite set of states, P : S × S → =-=[0, 1]-=- is a probability matrix such that � s ′ ∈S P(s, s′ ) = 1 for all s ∈ S, and L : S → 2AP is a labelling function which assigns to each state s ∈ S the set L(s) of atomic propositions that hold in s. A... |

15 | CSL model checking for the GreatSPN tool.
- D’Aprile, Donatelli, et al.
- 2004
(Show Context)
Citation Context ...otocols, biological process modeling, and quantum computing. Probabilistic model checking engines have been integrated in existing tool chains for widely used formalisms such as stochastic Petri nets =-=[11]-=-, Statemate [9], and the stochastic process algebra PEPA [24], and are used for a probabilistic extension of Promela [4]. The typical kind of properties that can be checked is time-bounded reachabilit... |

15 | Bisimulation minimization in an automata-theoretic verification framework
- Fisler, Vardi
- 1998
(Show Context)
Citation Context ...tween bisimulation and MTBDDs would unnecessarily complicate our study; such symbolic representations mostly grow under bisimulation minimisation [23]. Thanks to extensive studies by Fisler and Vardi =-=[16,17,18]-=-, it is known that bisimulation minimisation for LTL model checking and invariant verification leads to drastic state space reductions (up to logarithmic savings) but at a time penalty: the time to mi... |

13 |
B.: Compositional performability evaluation for Statemate
- Böde, Herbstritt, et al.
- 2006
(Show Context)
Citation Context ...cal process modeling, and quantum computing. Probabilistic model checking engines have been integrated in existing tool chains for widely used formalisms such as stochastic Petri nets [11], Statemate =-=[9]-=-, and the stochastic process algebra PEPA [24], and are used for a probabilistic extension of Promela [4]. The typical kind of properties that can be checked is time-bounded reachability properties—“D... |

13 |
Y.: Bisimulation minimization and symbolic model checking
- Fisler, Vardi
(Show Context)
Citation Context ...tween bisimulation and MTBDDs would unnecessarily complicate our study; such symbolic representations mostly grow under bisimulation minimisation [23]. Thanks to extensive studies by Fisler and Vardi =-=[16,17,18]-=-, it is known that bisimulation minimisation for LTL model checking and invariant verification leads to drastic state space reductions (up to logarithmic savings) but at a time penalty: the time to mi... |

12 | Safe on-the-fly steady-state detection for time-bounded reachability.
- Katoen, Zapreev
- 2006
(Show Context)
Citation Context ...l stems from the fact that the time bound (24000) is very large, resulting in many iterations. These verification times can be improved by incorporating an on-the-fly steady-state detection procedure =-=[30]-=-, but this is not further considered here. Simple P2P protocol [33]. This case study describes a simple peer-to-peer protocol based on BitTorrent—a “torrent” is a small file which contains metadata ab... |

11 |
An abstraction framework for mixed nondeterministic and probabilistic systems
- Huth
- 2004
(Show Context)
Citation Context ... pre-orders allow model aggregation prior to model checking, e. g., [7,39]. Recently proposed techniques include abstractions of probabilities by intervals combined with three-valued logics for DTMCs =-=[15,25,26]-=-, stochastic ordering techniques for CSL model checking [8], abstraction of MDPs by two-player stochastic games [32], and symmetry reduction [33]. The purpose of this paper is to empirically investiga... |

10 |
ProbMela and verification of Markov decision processes.
- Baier, Ciesinski, et al.
- 2005
(Show Context)
Citation Context ...cked. 1 Introduction Probabilistic model checking enjoys a rapid increase of interest from different communities. Software tools such as PRISM [31] (with about 4,000 downloads), MRMC [29], and LiQuor =-=[4]-=- support the verification of Markov chains or variants thereof that exhibit nondeterminism. They have been applied to case studies from areas such as randomised distributed algorithms, planning and AI... |

9 |
Model checking dependability attributes of wireless group communication
- Massink, Katoen, et al.
- 2004
(Show Context)
Citation Context ...e study are not so high, as its formal (stochastic Petri net) specification already exploits some lumping; e.g., workstations are modeled by anonymous tokens. IEEE 802.11 group communication protocol =-=[35]-=-. This is a variant of the centralized medium access protocol of the IEEE 802.11 standard for wireless local area networks. The protocol is centralized in the sense that medium access is controlled by... |

8 | Backward Bisimulation in Markov Chain Model Checking”,
- Sproston, Donatelli
- 2006
(Show Context)
Citation Context ...eneralised to MDPs [19], abstract interpretation has been applied to MDPs [36], and various bisimulation equivalences and simulation pre-orders allow model aggregation prior to model checking, e. g., =-=[7,39]-=-. Recently proposed techniques include abstractions of probabilities by intervals combined with three-valued logics for DTMCs [15,25,26], stochastic ordering techniques for CSL model checking [8], abs... |

7 |
J.-P.: On the use of model checking techniques for quantitative dependability evaluation
- Haverkort, Hermanns, et al.
- 2000
(Show Context)
Citation Context ...isimilarity. Due to the coarser initial partition, this quotient is constructed rather fast. In this case, verifying the original model is more time consuming. 4.2 Continuous time Workstation cluster =-=[22]-=-. This case study considers a system consisting of two clusters of workstations connected via a backbone. Each cluster consists of N workstations, connected in a star topology with a central switch th... |

7 |
J.P.: Model-Checking Algorithms for Continuous-Time Markov Chains
- Baier, Haverkort, et al.
- 2003
(Show Context)
Citation Context ...ov chains (DTMCs and CTMCs, for short), and variants thereof with costs. The advantages of probabilistic bisimulation [34] in this setting are manifold. It preserves the validity of PCTL [20] and CSL =-=[2,6]-=- formulas, variants of CTL for the discrete- and continuous-time probabilistic setting, respectively. It implies ordinary lumpability of Markov chains [10], an aggregation technique for Markov chains ... |

6 |
C.: Partial order reduction for Markov decision processes: a survey
- Groesser, Baier
- 2006
(Show Context)
Citation Context ...of probabilistic models, abstraction-refinement has been applied to reachability problems in MDPs [12], partial-order reduction techniques using Peled’s ample-set method have been generalised to MDPs =-=[19]-=-, abstract interpretation has been applied to MDPs [36], and various bisimulation equivalences and simulation pre-orders allow model aggregation prior to model checking, e. g., [7,39]. Recently propos... |

4 |
S.: Model checking of continuous-time Markov chains by closed-form bounding distributions
- Mamoun, Pekergin, et al.
- 2006
(Show Context)
Citation Context ..., [7,39]. Recently proposed techniques include abstractions of probabilities by intervals combined with three-valued logics for DTMCs [15,25,26], stochastic ordering techniques for CSL model checking =-=[8]-=-, abstraction of MDPs by two-player stochastic games [32], and symmetry reduction [33]. The purpose of this paper is to empirically investigate the effect of strong bisimulation minimisation in probab... |

3 | Solution of Large Markov Models using Lumping Techniques and Symbolic Data Structures - Derisavi - 2005 |