Abstract
This paper introduces means to specify system randomness within UML statecharts, and to verify probabilistic temporal properties over such enhanced statecharts which we call probabilistic UML statecharts. To achieve this, we develop a general recipe to extend a statechart semantics with discrete probability distributions, resulting in Markov decision processes as semantic models. We apply this recipe to the requirements-level UML semantics of [8]. Properties of interest for probabilistic statecharts are expressed in PCTL, a probabilistic variant of CTL for processes that exhibit both non-determinism and probabilities. Verification is performed using the model checker Prism. A model checking example shows the feasibility of the suggested approach.
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Christel Baier and Marta Kwiatkowska. Model checking for a probabilistic branching time logic with fairness. Distributed Computing, 11(3):125–155, 1998.
Michael von der Beeck. A comparison of statecharts variants. In H. Langmaack, W.-P. de Roever, and J. Vytopil, editors, Formal Techniques in Real-Time and Fault-Tolerant Systems:...proceedings, pages 128–148, Berlin, 1994. Springer.
Andrea Bianco and Luca de Alfaro. Model checking of probabilistic and nondeter-ministic systems. In P. S. Thiagarajan, editor, Foundations of Software Technology and Theoretical Computer Science:... proceedings, volume 1026 of LNCS, pages 499–513, Berlin, 1995. Springer.
Philip H. Crowley. Hawks, doves, and mixed-symmetry games. Journal of Theoretical Biology, 204(4):543–563, June 2000.
M. Dal Cin, G. Huszerl, and K. Kosmidis. Evaluation of dependability critical systems based on guarded statechart models. In 4th Int. Symp. on High Assurance Systems Engineering (HASE), pages 37–45. IEEE, 1999.
Werner Damm, Bernhard Josko, Hardi Hungar, and Amir Pnueli. A compositional real-time semantics of statemate designs. In Willem-Paul de Roever, Hans Langmaack, and Amir Pnueli, editors, Compositionality: the significant difference. COMPOS’ 97, volume 1536 of LNCS, pages 186–238, Berlin, 1998. Springer.
Pedro R. D’Argenio, Holger Hermanns, and Joost-Pieter Katoen. On generative parallel composition. In Christel Baier, Michael Huth, Marta Kwiatkowska, and Mark Ryan, editors, PROBMIV’98 First International Workshop on Probabilistic Methods in Verification: Indianapolis, Ind.... 1998, volume 22 of Electronic Notes in Theoretical Computer Science. Elsevier, 2000. URL: http://www.elsevier.nl/locate/entcs/volume22.html.
Rik Eshuis and Roel Wieringa. Requirements-level semantics for UML statecharts. In Scott F. Smith and Carolyn L. Talcott, editors, Formal Methods for Open Object-Based Distributed Systems IV:... FMOODS, pages 121–140, Boston, 2000. Kluwer Academic Publishers.
Stefania Gnesi, Diego Latella, and Mieke Massink. A stochastic extension of a behavioural subset of UML statechart diagrams. In L. Palagi and R. Bilof, editors, Fifth International Symposium on High-Assurance Systems Engineering (HASE), pages 55–64. IEEE Computer Society Press, 2000.
H. A. Hansson. Time and Probability in Formal Design of Distributed Systems. PhD thesis, University of Uppsala, 1991.
Hans Hansson and Bengt Jonsson. A logic for reasoning about time and reliability. Formal Aspects of Computing, 6:512–535, 1994.
David Harel and Eran Gery. Executable object modeling with statecharts. Computer, 30(7):31–42, July 1997. IEEE.
David Harel and Amnon Naamad. The STATEMATE semantics of statecharts. ACM Transactions on Software Engineering and Methodology, 5(4):293–333, 1996.
Peter King and Rob Pooley. Derivation of Petri net performance models from UML specifications of communications software. In Boudewijn R. Haverkort, Henrik C. Bohnenkamp, and Connie U. Smith, editors, Computer Performance Evaluation: Modelling Techniques and Tools;... TOOLS 2000, volume 1786 of LNCS, pages 262–276, Berlin, 2000. Springer.
Marta Kwiatkowska, Gethin Norman, and David Parker. Probabilistic symbolic model checking with prism: A hybrid approach. In Joost-Pieter Katoen and Perdita Stevens, editors, Tools and Algorithms for the Construction and Analysis of Algorithms:.. TACAS, volume 2280 of LNCS, pages 52–66, Berlin, 2002. Springer.
C. Lindemann, A. Thümmler, A. Klemm, M. Lohmann, and O. P. Waldhorst. Quantitative system evaluation with DSPNexpress 2000. In Workshop on Software and Performance (WOSP), pages 12–17. ACM, 2000.
J. Maynard Smith and G. R. Price. The logic of animal conflict. Nature, 246, November 1973.
S. McMenamin and J. Palmer. Essential Systems Analysis. Yourdon Press, New York, 1984.
Martin L. Puterman. Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, New York, 1994.
R. Segala and N. Lynch. Probabilistic simulations for probabilistic processes. Nordic Journal of Computing, 2:250–273, 1995.
A. N. Shiryaev. Probability, volume 95 of Graduate texts in mathematics. Springer, New York, 1996.
UML Revision Task Force. OMG UML Specification 1.3. Object Management Group, 1999. http://www.omg.org/cgi-bin/doc?ad/99-06-08.
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Jansen, D.N., Hermanns, H., Katoen, JP. (2002). A Probabilistic Extension of UML Statecharts. In: Damm, W., Olderog, E.R. (eds) Formal Techniques in Real-Time and Fault-Tolerant Systems. FTRTFT 2002. Lecture Notes in Computer Science, vol 2469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45739-9_21
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