Abstract
In this talk we will discuss recent work on the modeling and algorithmic analysis of systems involving recursion and probability. There has been intense activity recently in the study of such systems [2,3,10,11,13,14,15,16,17]. The primary motivation comes from the analysis of probabilistic programs with procedures. Probability can arise either due to randomizing steps in the program, or it may reflect statistical assumptions on the behaviour of the program, under which we want to investigate its properties.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alur, R., Benedikt, M., Etessami, K., Godefroid, P., Reps, T.W., Yannakakis, M.: Analysis of recursive state machines. ACM Trans. Progr. Lang. Sys. 27, 786–818 (2005)
Brázdil, T., Kučera, A., Esparza, J.: Analysis and prediction of the long-run behavior of probabilistic sequential programs with recursion. In: Proc. of FOCS 2005 (2005)
Brázdil, T., Kučera, A., Stražovský, O.: Decidability of temporal properties of probabilistic pushdown automata. In: Proc. of STACS 2005 (2005)
Basu, S., Pollack, R., Roy, M.F.: On the combinatorial and algebraic complexity of quantifier elimination. J. ACM 43(6), 1002–1045 (1996)
Canny, J.: Some algebraic and geometric computations in PSPACE. In: Prof. of 20th ACM STOC, pp. 460–467 (1988)
Condon, A.: The complexity of stochastic games. Inf. & Comp. 96(2), 203–224 (1992)
Courcoubetis, C., Yannakakis, M.: The complexity of probabilistic verification. Journal of the ACM 42(4), 857–907 (1995)
Courcoubetis, C., Yannakakis, M.: Markov decision processes and regular events. IEEE Trans. on Automatic Control 43(10), 1399–1418 (1998)
de Alfaro, L., Kwiatkowska, M., Norman, G., Parker, D., Segala, R.: Symbolic model checking of probabilistic processes using MTBDDs and the kronecker representation. In: Schwartzbach, M.I., Graf, S. (eds.) TACAS 2000. LNCS, vol. 1785, pp. 395–410. Springer, Heidelberg (2000)
Esparza, J., Kučera, A., Mayr, R.: Model checking probabilistic pushdown automata. In: Proc. of 19th IEEE LICS 2004 (2004)
Esparza, J., Kučera, A., Mayr, R.: Quantitative analysis of probabilistic pushdown automata: expectations and variances. In: Proc. of 20th IEEE LICS (2005)
Everett, C.J., Ulam, S.: Multiplicative systems, part i., ii, and iii. Technical Report 683,690,707, Los Alamos Scientific Laboratory (1948)
Etessami, K., Yannakakis, M.: Recursive Markov chains, stochastic grammars, and monotone systems of non-linear equations. In: Diekert, V., Durand, B. (eds.) STACS 2005. LNCS, vol. 3404, pp. 340–352. Springer, Heidelberg (2005)
Etessami, K., Yannakakis, M.: Algorithmic verification of recursive probabilistic state machines. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 253–270. Springer, Heidelberg (2005)
Etessami, K., Yannakakis, M.: Recursive Markov Decision Processes and Recursive Stochastic Games. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 891–903. Springer, Heidelberg (2005)
Etessami, K., Yannakakis, M.: Checking LTL Properties of Recursive Markov Chains. In: Proc. 2nd Intl. Conf. on Quantitative Evaluation of Systems. IEEE, Los Alamitos (2005)
Etessami, K., Yannakakis, M.: Efficient Analysis of Classes of Recursive Markov Decision Processes and Stochastic Games (submitted)
Feinberg, E., Shwartz, A. (eds.): Handbook of Markov Decision Processes. Kluwer, Dordrecht (2002)
Filar, J., Vrieze, K.: Competitive Markov Decision Processes. Springer, Heidelberg (1997)
Garey, M.R., Graham, R.L., Johnson, D.S.: Some NP-complete geometric problems. In: 8th ACM Symp. on Theory of Computing, pp. 10–22 (1976)
Harris, T.E.: The Theory of Branching Processes. Springer, Heidelberg (1963)
Jagers, P.: Branching Processes with Biological Applications. Wiley, Chichester (1975)
Kolmogorov, A.N., Sevastyanov, B.A.: The calculation of final probabilities for branching random processes. Dokl. Akad. Nauk SSSR 56, 783–786 (1947) (Russian)
Kwiatkowska, M.: Model checking for probability and time: from theory to practice. In: 18th IEEE LICS, pp. 351–360 (2003)
Manning, C., Schütze, H.: Foundations of Statistical Natural Language Processing. MIT Press, Cambridge (1999)
Paz, A.: Introduction to Probabilistic Automata. Academic Press, London (1971)
Pnueli, A., Zuck, L.D.: Probabilistic verification. Inf. and Comp. 103(1), 1–29 (1993)
Puterman, M.L.: Markov Decision Processes. Wiley, Chichester (1994)
Renegar, J.: On the computational complexity and geometry of the first-order theory of the reals, parts I-III. J. Symb. Comp. 13(3), 255–352 (1992)
Sakakibara, Y., Brown, M., Hughey, R., Mian, I.S., Sjolander, K., Underwood, R., Haussler, D.: Stochastic context-free grammars for tRNA modeling. Nucleic Acids Research 22(23), 5112–5120 (1994)
Sevastyanov, B.A.: The theory of branching processes. Uspehi Mathemat. Nauk 6, 47–99 (1951) (Russian)
Tiwari, P.: A problem that is easier to solve on the unit-cost algebraic ram. Journal of Complexity, 393–397 (1992)
Vardi, M.: Automatic verification of probabilistic concurrent finite-state programs. In: Proc. of 26th IEEE FOCS, pp. 327–338 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Etessami, K., Yannakakis, M. (2005). Probability and Recursion. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_2
Download citation
DOI: https://doi.org/10.1007/11602613_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30935-2
Online ISBN: 978-3-540-32426-3
eBook Packages: Computer ScienceComputer Science (R0)