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.
- A. Aziz, K. Sanwal, V. Singhal, and R. Brayton. Model-checking continuous-time markov chains. ACM Trans. Comput. Logic, 1(1):162--170, 2000.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- R. E. Bryant. Graph-based algorithms for boolean function manipulation. IEEE TC, 35(8):677--691, Aug. 1986.]] Google ScholarDigital Library
- P. Buchholz. An adaptive decomposition approach for the analysis of stochastic Petri nets. In Proc. DSN, pages 647--656, June 2002.]] Google ScholarDigital Library
- 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.]]Google ScholarCross Ref
- P. Buchholz, J. P. Katoen, P. Kemper, and C. Tepper. Model-checking large structured Markov chains. JLAP, 56(1/2):69--97, 2003.]]Google Scholar
- P. Buchholz and P. Kemper. Numerical analysis of stochastic marked graphs. In Proc. PNPM, pages 32--41, Oct. 1995. IEEE CS Press.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- 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.]]Google ScholarCross Ref
- 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.]] Google ScholarDigital Library
- M. Davio. Kronecker products and shuffle algebra. IEEE TC, C-30:116--125, Feb. 1981.]]Google ScholarCross Ref
- 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.]] Google ScholarDigital Library
- 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.]]Google ScholarCross Ref
- S. Donatelli. Superposed generalized stochastic Petri nets: definition and efficient solution. In Proc. ICATPN, LNCS 815, pages, 258--277, June 1994. Springer-Verlag.]] Google ScholarDigital Library
- P. Fernandes, B. Plateau, and W. J. Stewart. Efficient descriptor-vector multiplication in stochastic automata networks. JACM, 45(3):381--414, 1998.]] Google ScholarDigital Library
- 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.]]Google Scholar
- 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.]]Google Scholar
- P. Kemper. Numerical analysis of superposed GSPNs. IEEE TSE, 22(4):615--628, Sept. 1996.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- A. S. Miner. Efficient state space generation of GSPNs using decision diagrams. In Proc. DSN, pages 637--646, June 2002.]] Google ScholarDigital Library
- A. S. Miner. Saturation for a general class of models. In Proc. QEST, pages 282--291, Sept. 2004.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- 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.]] Google ScholarDigital Library
- B. Plateau. On the stochastic structure of parallelism and synchronisation models for distributed algorithms. In Proc. SIGMETRICS, pages 147--153, May 1985.]] Google ScholarDigital Library
- A. Pnueli. The temporal logic of programs. In Proc. FOCS, pages 46--57. IEEE CS Press, Nov. 1977.]]Google ScholarDigital Library
Index Terms
- Implicit data structures for logic and stochastic systems analysis
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