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Implicit data structures for logic and stochastic systems analysis

Published: 01 March 2005 Publication History

Abstract

Both logic and stochastic analysis have strong theoretical underpinnings, but they have been traditionally relegated to separate areas of computer science, the former focusing on logic and discrete algorithms, the latter on exact or approximate numerical methods. In the last few years, though, there has been a convergence of research in these two areas, due to the realization that data structures used in one area can benefit the other and that, by merging the goals of the two areas, a more integrated approach to system analysis can be derived. In this paper, we describe some of the beneficial interactions between the two, and some of the research challenges ahead.

References

[1]
A. Aziz, K. Sanwal, V. Singhal, and R. Brayton. Model-checking continuous-time markov chains. ACM Trans. Comput. Logic, 1(1):162--170, 2000.]]
[2]
C. Baier, B. Haverkort, H. Hermanns, and J.-P. Katoen. Model checking algorithms for continuous-time Markov chains. IEEE TSE, 29(6):524--541, June 2003.]]
[3]
M. Bozga and O. Maler. On the representation of probabilities over structured domains. In Proc. CAV, LNCS 1633, pages 261--273, July 1999. Springer-Verlag.]]
[4]
R. E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE TC, 35(8):677--691, Aug. 1986.]]
[5]
P. Buchholz. An adaptive decomposition approach for the analysis of stochastic Petri nets. In Proc. DSN, pages 647--656, June 2002.]]
[6]
P. Buchholz, G. Ciardo, S. Donatelli, and P. Kemper. Complexity of memory-efficient Kronecker operations with applications to the solution of Markov models. INFORMS J. Comp., 12(3):203--222, 2000.]]
[7]
P. Buchholz, J. P. Katoen, P. Kemper, and C. Tepper. Model-checking large structured Markov chains. JLAP, 56(1/2):69--97, 2003.]]
[8]
P. Buchholz and P. Kemper. Numerical analysis of stochastic marked graphs. In Proc. PNPM, pages 32--41, Oct. 1995. IEEE CS Press.]]
[9]
J. R. Burch, E. M. Clarke, K. L. McMillan, D. L. Dill, and L. J. Hwang. Symbolic model checking: 1020 states and beyond. Information and Computation, 98:142--170, 1992.]]
[10]
G. Ciardo, G. Luettgen, and R. Siminiceanu. Saturation: An efficient iteration strategy for symbolic state space generation. In Proc. TACAS, LNCS 2031, pages 328--342, Apr. 2001. Springer-Verlag.]]
[11]
G. Ciardo and A. S. Miner. A data structure for the efficient Kronecker solution of GSPNs. In Proc. PNPM, pages 22--31, Sept. 1999. IEEE CS Press.]]
[12]
G. Ciardo and R. Siminiceanu. Using edge-valued decision diagrams for symbolic generation of shortest paths. In Proc. FMCAD, LNCS 2517, pages 256--273, Nov. 2002. Springer-Verlag.]]
[13]
G. Ciardo and R. Siminiceanu. Structural symbolic CTL model checking of asynchronous systems. In Proc. CAV, LNCS 2725, pages 40--53, July 2003. Springer-Verlag.]]
[14]
E. M. Clarke and E. A. Emerson. Design and synthesis of synchronization skeletons using branching time temporal logic. In Proc. IBM Workshop on Logics of Programs, LNCS 131, pages 52--71. Springer-Verlag, 1981.]]
[15]
M. Davio. Kronecker products and shuffle algebra. IEEE TC, C-30:116--125, Feb. 1981.]]
[16]
D. D. Deavours and W. H. Sanders. "On-the-fly" solution techniques for stochastic Petri nets and extensions. In Proc. PNPM, pages 132--141, June 1997. IEEE CS Press.]]
[17]
S. Derisavi, P. Kemper, and W. H. Sanders. Symbolic state-space exploration and numerical analysis of state-sharing composed models. Linear Algebra and Its Applications, 386C:137--166, 2004.]]
[18]
S. Donatelli. Superposed generalized stochastic Petri nets: definition and efficient solution. In Proc. ICATPN, LNCS 815, pages, 258--277, June 1994. Springer-Verlag.]]
[19]
P. Fernandes, B. Plateau, and W. J. Stewart. Efficient descriptor-vector multiplication in stochastic automata networks. JACM, 45(3):381--414, 1998.]]
[20]
H. Hermanns, J. Meyer-Kayser, and M. Siegle. Multi terminal binary decision diagrams to represent and analyse continuous-time Markov chains. In Proc. NSMC, pages 188--207, Sept. 1999. Prensas Universitarias de Zaragoza, Spain.]]
[21]
T. Kam, T. Villa, R. Brayton, and A. Sangiovanni-Vincentelli. Multi-valued decision diagrams: theory and applications. Multiple-Valued Logic, 4(1--2):9--62, 1998.]]
[22]
P. Kemper. Numerical analysis of superposed GSPNs. IEEE TSE, 22(4):615--628, Sept. 1996.]]
[23]
M. Z. Kwiatkowska, G. Norman, and D. Parker. Probabilistic symbolic model checking with PRISM: a hybrid approach. Software Tools for Technology Transfer, 6(2):128--142, 2004.]]
[24]
A. S. Miner. Efficient state space generation of GSPNs using decision diagrams. In Proc. DSN, pages 637--646, June 2002.]]
[25]
A. S. Miner. Saturation for a general class of models. In Proc. QEST, pages 282--291, Sept. 2004.]]
[26]
A. S. Miner and G. Ciardo. Efficient reachability set generation and storage using decision diagrams. In Proc. ICATPN, LNCS 1639, pages 6--25, June 1999. Springer-Verlag.]]
[27]
A. S. Miner, G. Ciardo, and S. Donatelli. Using the exact state space of a Markov model to compute approximate stationary measures. In Proc. SIGMETRICS, pages 207--216, June 2000.]]
[28]
B. Plateau. On the stochastic structure of parallelism and synchronisation models for distributed algorithms. In Proc. SIGMETRICS, pages 147--153, May 1985.]]
[29]
A. Pnueli. The temporal logic of programs. In Proc. FOCS, pages 46--57. IEEE CS Press, Nov. 1977.]]

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  • (2009)Hierarchical Set Decision Diagrams and Regular ModelsProceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,10.1007/978-3-642-00768-2_1(1-15)Online publication date: 27-Mar-2009

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cover image ACM SIGMETRICS Performance Evaluation Review
ACM SIGMETRICS Performance Evaluation Review  Volume 32, Issue 4
March 2005
45 pages
ISSN:0163-5999
DOI:10.1145/1059816
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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 March 2005
Published in SIGMETRICS Volume 32, Issue 4

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  • (2009)Hierarchical Set Decision Diagrams and Regular ModelsProceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,10.1007/978-3-642-00768-2_1(1-15)Online publication date: 27-Mar-2009

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