Scenario-Based Verification of Uncertain MDPs
303
References
1. Abraham Charnes and William W Cooper. Chance-Constrained Programming.
Management science, 6(1):73–79, 1959.
2. Amir Pnueli. The Temporal Logic of Programs. In FOCS, pages 46–57, 1977.
3. James Aspnes and Maurice Herlihy. Fast Randomized Consensus Using Shared
Memory. Journal of Algorithms, 15(1):441–460, 1990.
4. Hans Hansson and Bengt Jonsson. A Logic for Reasoning about Time and Reliability.
Formal Aspects of Computing, 6(5):512–535, 1994.
5. L. Helmink, M. Sellink, and F. Vaandrager. Proof-Checking a Data Link Protocol.
In TYPES, volume 806 of LNCS, pages 127–165. Springer, 1994.
6. Anthony Cassandra, Michael L Littman, and Nevin L Zhang. Incremental Pruning:
A Simple, Fast, Exact Method for Partially Observable Markov Decision Processes.
In UAI, pages 54–61, 1997.
7. Robert Givan, Sonia Leach, and Thomas Dean. Bounded-Parameter Markov
Decision Processes. Artificial Intelligence, 122(1-2):71–109, 2000.
8. Jie Han and Pieter Jonker. A System Architecture Solution for Unreliable Nanoelectronic Devices. IEEE Transactions on Nanotechnology, 1:201–208, 2002.
9. Christel Baier, Boudewijn R. Haverkort, Holger Hermanns, and Joost-Pieter Katoen.
Model-Checking Algorithms for Continuous-Time Markov Chains. IEEE Trans.
Software Eng., 29(6):524–541, 2003.
10. Joelle Pineau, Geoff Gordon, and Sebastian Thrun. Point-Based Value Iteration:
an Anytime Algorithm for POMDPs. In IJCAI, pages 1025–1030, 2003.
11. Conrado Daws. Symbolic and Parametric Model Checking of Discrete-Time Markov
chains. In ICTAC, volume 3407 of LNCS, pages 280–294. Springer, 2004.
12. Vitaly Shmatikov. Probabilistic Analysis of an Anonymity System. Journal of
Computer Security, 12(3-4):355–377, 2004.
13. G.C. Calafiore and M.C. Campi. Uncertain Convex Programs: Randomized Solutions
and Confidence Levels. Mathematical Programming, 102(1):25–46, 2005.
14. Arnab Nilim and Laurent El Ghaoui. Robust Control of Markov Decision Processes
with Uncertain Transition Matrices. Operations Research, 53(5):780–798, 2005.
15. Giuseppe C. Calafiore and Marco C. Campi. The Scenario Approach to Robust
Control Design. IEEE Trans. Automat. Contr., 51(5):742–753, 2006.
16. Marco C. Campi and Simone Garatti. The Exact Feasibility of Randomized Solutions
of Uncertain Convex Programs. SIAM Journal on Optimization, 19(3):1211–1230,
2008.
17. Ernst Moritz Hahn, Holger Hermanns, and Lijun Zhang. Probabilistic Reachability
for Parametric Markov Models. STTT, 13(1):3–19, 2010.
18. Dimitris Bertsimas, David B Brown, and Constantine Caramanis. Theory and
Applications of Robust Optimization. SIAM review, 53(3):464–501, 2011.
19. Marco C Campi and Simone Garatti. A Sampling-and-Discarding Approach to
Chance-Constrained Optimization: Feasibility and Optimality. Journal of Optimization Theory and Applications, 148(2):257–280, 2011.
20. Benoˆ ıt Delahaye, Kim G. Larsen, Axel Legay, Mikkel L. Pedersen, and Andrzej
Wasowski. Decision problems for interval Markov chains. In LATA, volume 6638 of
LNCS, pages 274–285. Springer, 2011.
21. Marta Kwiatkowska, Gethin Norman, and David Parker. PRISM 4.0: Verification
of Probabilistic Real-Time Systems. In CAV, volume 6806 of LNCS, pages 585–591.
Springer, 2011.
303
References
1. Abraham Charnes and William W Cooper. Chance-Constrained Programming.
Management science, 6(1):73–79, 1959.
2. Amir Pnueli. The Temporal Logic of Programs. In FOCS, pages 46–57, 1977.
3. James Aspnes and Maurice Herlihy. Fast Randomized Consensus Using Shared
Memory. Journal of Algorithms, 15(1):441–460, 1990.
4. Hans Hansson and Bengt Jonsson. A Logic for Reasoning about Time and Reliability.
Formal Aspects of Computing, 6(5):512–535, 1994.
5. L. Helmink, M. Sellink, and F. Vaandrager. Proof-Checking a Data Link Protocol.
In TYPES, volume 806 of LNCS, pages 127–165. Springer, 1994.
6. Anthony Cassandra, Michael L Littman, and Nevin L Zhang. Incremental Pruning:
A Simple, Fast, Exact Method for Partially Observable Markov Decision Processes.
In UAI, pages 54–61, 1997.
7. Robert Givan, Sonia Leach, and Thomas Dean. Bounded-Parameter Markov
Decision Processes. Artificial Intelligence, 122(1-2):71–109, 2000.
8. Jie Han and Pieter Jonker. A System Architecture Solution for Unreliable Nanoelectronic Devices. IEEE Transactions on Nanotechnology, 1:201–208, 2002.
9. Christel Baier, Boudewijn R. Haverkort, Holger Hermanns, and Joost-Pieter Katoen.
Model-Checking Algorithms for Continuous-Time Markov Chains. IEEE Trans.
Software Eng., 29(6):524–541, 2003.
10. Joelle Pineau, Geoff Gordon, and Sebastian Thrun. Point-Based Value Iteration:
an Anytime Algorithm for POMDPs. In IJCAI, pages 1025–1030, 2003.
11. Conrado Daws. Symbolic and Parametric Model Checking of Discrete-Time Markov
chains. In ICTAC, volume 3407 of LNCS, pages 280–294. Springer, 2004.
12. Vitaly Shmatikov. Probabilistic Analysis of an Anonymity System. Journal of
Computer Security, 12(3-4):355–377, 2004.
13. G.C. Calafiore and M.C. Campi. Uncertain Convex Programs: Randomized Solutions
and Confidence Levels. Mathematical Programming, 102(1):25–46, 2005.
14. Arnab Nilim and Laurent El Ghaoui. Robust Control of Markov Decision Processes
with Uncertain Transition Matrices. Operations Research, 53(5):780–798, 2005.
15. Giuseppe C. Calafiore and Marco C. Campi. The Scenario Approach to Robust
Control Design. IEEE Trans. Automat. Contr., 51(5):742–753, 2006.
16. Marco C. Campi and Simone Garatti. The Exact Feasibility of Randomized Solutions
of Uncertain Convex Programs. SIAM Journal on Optimization, 19(3):1211–1230,
2008.
17. Ernst Moritz Hahn, Holger Hermanns, and Lijun Zhang. Probabilistic Reachability
for Parametric Markov Models. STTT, 13(1):3–19, 2010.
18. Dimitris Bertsimas, David B Brown, and Constantine Caramanis. Theory and
Applications of Robust Optimization. SIAM review, 53(3):464–501, 2011.
19. Marco C Campi and Simone Garatti. A Sampling-and-Discarding Approach to
Chance-Constrained Optimization: Feasibility and Optimality. Journal of Optimization Theory and Applications, 148(2):257–280, 2011.
20. Benoˆ ıt Delahaye, Kim G. Larsen, Axel Legay, Mikkel L. Pedersen, and Andrzej
Wasowski. Decision problems for interval Markov chains. In LATA, volume 6638 of
LNCS, pages 274–285. Springer, 2011.
21. Marta Kwiatkowska, Gethin Norman, and David Parker. PRISM 4.0: Verification
of Probabilistic Real-Time Systems. In CAV, volume 6806 of LNCS, pages 585–591.
Springer, 2011.