## How to Specify and Verify the Long-Run Average Behavior of Probabilistic Systems (1998)

Venue: | In Proc. LICS'98 |

Citations: | 38 - 3 self |

### BibTeX

@INPROCEEDINGS{Alfaro98howto,

author = {Luca De Alfaro},

title = {How to Specify and Verify the Long-Run Average Behavior of Probabilistic Systems},

booktitle = {In Proc. LICS'98},

year = {1998},

pages = {454--465}

}

### Years of Citing Articles

### OpenURL

### Abstract

Long-run average properties of probabilistic systems refer to the average behavior of the system, measured over a period of time whose length diverges to infinity. These properties include many relevant performance and reliability indices, such as system throughput, average response time, and mean time between failures. In this paper, we argue that current formal specification methods cannot be used to specify long-run average properties of probabilistic systems. To enable the specification of these properties, we propose an approach based on the concept of experiments. Experiments are labeled graphs that can be used to describe behavior patterns of interest, such as the request for a resource followed by either a grant or a rejection. Experiments are meant to be performed infinitely often, and it is possible to specify their long-run average outcome or duration. We propose simple extensions of temporal logics based on experiments, and we present model-checking algorithms for the verif...

### Citations

318 |
Dynamic programming and optimal control
- Bertsekas
(Show Context)
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- Segala, Lynch
- 1995
(Show Context)
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258 | A Class of Generalized Stochastic Petri Nets for the Performance Evaluation of Multiprocessor Systems”, retrieved from http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1 .90.8002 on 17/5/2013
- Marsan, Balbo, et al.
(Show Context)
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- Hansson, Jonsson
- 1994
(Show Context)
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230 |
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- Segala
- 1995
(Show Context)
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215 |
Automatic verification of probabilistic concurrent finite state programs
- Vardi
- 1985
(Show Context)
Citation Context ...m behaviors, we need to specify the criteria with which the actions are chosen. To this end, we use the concept of policy [14], closely related to the adversaries of [29, 28] and to the schedulers of =-=[31, 27]-=-. A policy j is a set of conditional probabilities Q j (a j s 0 s 1 \Delta \Delta \Delta s n ), for all ns0, s 0 ; s 1 ; : : : ; s n 2 S and a 2 A(sn ). According to policy j, after the finite prefix ... |

199 | Model checking of probabilistic and nondeterministic systems
- Bianco, Alfaro
- 1995
(Show Context)
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132 |
Finite State Markovian Decision Processes
- Derman
- 1970
(Show Context)
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115 |
Formal verification of probabilistic systems
- Alfaro
- 1997
(Show Context)
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- Baier, Kwiatkowska
- 1998
(Show Context)
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110 | M.: Multiprocessor and distributed systems design: The integration of functional specification and performance analysis using stochastic process algebras
- Gotz, Herzog, et al.
- 1993
(Show Context)
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84 | It usually works: The temporal logic of stochastic systems
- Aziz, Singhal, et al.
- 1995
(Show Context)
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77 |
Computer systems performance evaluation
- Ferrari
- 1978
(Show Context)
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A logic for reasoning about time and probability
- Hansson, Jonsson
- 1994
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Markov decision processes and regular events
- Courcoubetis, Yannakakis
- 1990
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50 |
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- Cleaveland, Dayar, et al.
- 1999
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- Bernardo, Gorrieri
- 1996
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- Landweber
- 1969
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- 1991
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- Larsen, Skou
- 1989
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