CIAA 2017: Implementation and Application of Automata pp 1-13 | Cite as
On the Complexity of Determinizing Monitors
Conference paper
First Online:
Abstract
We examine the determinization of monitors. We demonstrate that every monitor is equivalent to a deterministic one, which is at most doubly exponential in size with respect to the original monitor. When monitors are described as CCS-like processes, this doubly-exponential bound is optimal. When (deterministic) monitors are described as finite automata (as their LTS), then they can be exponentially more succinct than their CCS process form.
References
- 1.Aceto, L., Achilleos, A., Francalanza, A., Ingólfsdóttir, A., Kjartansson, S.Ö.: Determinizing monitors for HML with recursion. arXiv preprint arXiv:1611.10212 (2016)
- 2.Barringer, H., Falcone, Y., Havelund, K., Reger, G., Rydeheard, D.: Quantified event automata: towards expressive and efficient runtime monitors. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 68–84. Springer, Heidelberg (2012). doi: 10.1007/978-3-642-32759-9_9 CrossRefGoogle Scholar
- 3.Berkovich, S., Bonakdarpour, B., Fischmeister, S.: Runtime verification with minimal intrusion through parallelism. Formal Methods Syst. Des. 46(3), 317–348 (2015)CrossRefMATHGoogle Scholar
- 4.Björklund, H., Martens, W.: The tractability frontier for NFA minimization. J. Comput. Syst. Sci. 78(1), 198–210 (2012)MathSciNetCrossRefMATHGoogle Scholar
- 5.Bocchi, L., Chen, T.-C., Demangeon, R., Honda, K., Yoshida, N.: Monitoring networks through multiparty session types. In: Beyer, D., Boreale, M. (eds.) FMOODS/FORTE -2013. LNCS, vol. 7892, pp. 50–65. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38592-6_5 CrossRefGoogle Scholar
- 6.Cassar, I., Francalanza, A.: On implementing a monitor-oriented programming framework for actor systems. In: Ábrahám, E., Huisman, M. (eds.) IFM 2016. LNCS, vol. 9681, pp. 176–192. Springer, Cham (2016). doi: 10.1007/978-3-319-33693-0_12 CrossRefGoogle Scholar
- 7.Chrobak, M.: Finite automata and unary languages. Theor. Comput. Sci. 47, 149–158 (1986)MathSciNetCrossRefMATHGoogle Scholar
- 8.dAmorim, M., Roşu, G.: Efficient monitoring of \(\omega \)-languages. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 364–378. Springer, Heidelberg (2005). doi: 10.1007/11513988_36 CrossRefGoogle Scholar
- 9.Fraigniaud, P., Rajsbaum, S., Travers, C.: On the number of opinions needed for fault-tolerant run-time monitoring in distributed systems. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 92–107. Springer, Cham (2014). doi: 10.1007/978-3-319-11164-3_9 Google Scholar
- 10.Francalanza, A.: A theory of monitors. In: Jacobs, B., Löding, C. (eds.) FoSSaCS 2016. LNCS, vol. 9634, pp. 145–161. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-49630-5_9 CrossRefGoogle Scholar
- 11.Francalanza, A., Aceto, L., Ingolfsdottir, A.: On verifying hennessy-milner logic with recursion at runtime. In: Bartocci, E., Majumdar, R. (eds.) RV 2015. LNCS, vol. 9333, pp. 71–86. Springer, Cham (2015). doi: 10.1007/978-3-319-23820-3_5 CrossRefGoogle Scholar
- 12.Gramlich, G., Schnitger, G.: Minimizing NFA’s and regular expressions. J. Comput. Syst. Sci. 73(6), 908–923 (2007)MathSciNetCrossRefMATHGoogle Scholar
- 13.Gruber, H., Holzer, M.: Inapproximability of nondeterministic state and transition complexity assuming P \(\ne \) NP. In: Harju, T., Karhumäki, J., Lepistö, A. (eds.) DLT 2007. LNCS, vol. 4588, pp. 205–216. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-73208-2_21 CrossRefGoogle Scholar
- 14.Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Comput. 22(6), 1117–1141 (1993)MathSciNetCrossRefMATHGoogle Scholar
- 15.Kozen, D.: Results on the propositional \(\mu \)-calculus. Theor. Comput. Sci. 27(3), 333–354 (1983)MathSciNetCrossRefMATHGoogle Scholar
- 16.Larsen, K.G.: Proof systems for satisfiability in Hennessy-Milner logic with recursion. Theor. Comput. Sci. 72(2&3), 265–288 (1990)MathSciNetCrossRefMATHGoogle Scholar
- 17.Leucker, M., Schallhart, C.: A brief account of runtime verification. J. Logic Algebraic Program. 78(5), 293–303 (2009)CrossRefMATHGoogle Scholar
- 18.Luo, Q., Roşu, G.: EnforceMOP: a runtime property enforcement system for multithreaded programs. In: International Symposium on Software Testing and Analysis, New York, USA, pp. 156–166 (2013)Google Scholar
- 19.Meyer, A.R., Fischer, M.J.: Economy of description by automata, grammars, and formal systems. In: 12th Annual Symposium on Switching and Automata Theory (1971)Google Scholar
- 20.Milner, R. (ed.): A Calculus of Communicating Systems. Springer, Heidelberg (1980)MATHGoogle Scholar
- 21.Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3(2), 114–125 (1959)MathSciNetCrossRefMATHGoogle Scholar
- 22.Rabinovich, A.: A complete axiomatisation for trace congruence of finite state behaviors. In: Brookes, S., Main, M., Melton, A., Mislove, M., Schmidt, D. (eds.) MFPS 1993. LNCS, vol. 802, pp. 530–543. Springer, Heidelberg (1994). doi: 10.1007/3-540-58027-1_25 CrossRefGoogle Scholar
- 23.Schneider, F.B.: Enforceable security policies. ACM Trans. Inf. Syst. Secur. (TISSEC) 3(1), 30–50 (2000)CrossRefGoogle Scholar
- 24.Sen, K., Vardhan, A., Agha, G., Roşu, G.: Efficient decentralized monitoring of safety in distributed systems. In: International Conference on Software Engineering, pp. 418–427 (2004)Google Scholar
- 25.Sipser, M.: Introduction to the Theory of Computation, Computer Science. PWS Publishing Company (1997)Google Scholar
- 26.Vardi, M.Y., Wolper, P.: Reasoning about infinite computations. Inf. Comput. 115(1), 1–37 (1994)MathSciNetCrossRefMATHGoogle Scholar
- 27.Yamagata, Y., Artho, C., Hagiya, M., Inoue, J., Ma, L., Tanabe, Y., Yamamoto, M.: Runtime monitoring for concurrent systems. In: Falcone, Y., Sánchez, C. (eds.) RV 2016. LNCS, vol. 10012, pp. 386–403. Springer, Cham (2016). doi: 10.1007/978-3-319-46982-9_24 CrossRefGoogle Scholar
Copyright information
© Springer International Publishing AG 2017