Abstract
This paper develops a Multiset Rewriting language with explicit time for the specification and analysis of Time-Sensitive Distributed Systems (TSDS). Goals are often specified using explicit time constraints. A good trace is an infinite trace in which the goals are satisfied perpetually despite possible interference from the environment. In our previous work [14], we discussed two desirable properties of TSDSes, realizability (there exists a good trace) and survivability (where, in addition, all admissible traces are good). Here we consider two additional properties, recoverability (all compliant traces do not reach points-of-no-return) and reliability (the system can always continue functioning using a good trace). Following [14], we focus on a class of systems called Progressing Timed Systems (PTS), where intuitively only a finite number of actions can be carried out in a bounded time period. We prove that for this class of systems the properties of recoverability and reliability coincide and are PSPACE-complete. Moreover, if we impose a bound on time (as in bounded model-checking), we show that for PTS the reliability property is in the \(\varPi _2^p\) class of the polynomial hierarchy, a subclass of PSPACE. We also show that the bounded survivability is both NP-hard and coNP-hard.
Dedicated to Joshua Guttman with gratitude for his inspiration and friendly and insightful discussions.
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
Notes
- 1.
For simplicity, in the rest of the paper, for properties of systems and configurations, we will not always explicitly state the critical configuration specification, initial configuration, and/or time samplingwith respect to which the property is considered. For example, when it is clear from the context, we simply say that a system satisfies \(Z\) property or that it is realizable.
Also, when for a property of an MSR \(\mathcal {T}\) we only consider traces that use the l.t.s., we also say that \(\mathcal {T}\) uses the lazy time sampling.
References
Alpern, B., Schneider, F.B.: Recognizing safety and liveness. Distrib. Comput. 2(3), 117–126 (1987)
Alur, R., Henzinger, T.A.: Logics and models of real time: a survey. In: Real-Time: Theory in Practice, REX Workshop, pp. 74–106 (1991)
Alur, R., Madhusudan, P.: Decision problems for timed automata: a survey. In: SFM, pp. 1–24 (2004)
Cárdenas, A.A., Amin, S., Sastry, S.: Secure control: Towards survivable cyber-physical systems. In: ICDCS, pp. 495–500 (2008)
Cervesato, I., Durgin, N.A., Lincoln, P., Mitchell, J.C., Scedrov, A.: A meta-notation for protocol analysis. In: CSFW, pp. 55–69 (1999)
Clarkson, M.R., Schneider, F.B.: Hyperproperties. J. Comput. Secur. 18(6), 1157–1210 (2010)
Clavel, M., et al.: All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71999-1
Dolev, D., Yao, A.: On the security of public key protocols. IEEE Trans. Inf. Theor. 29(2), 198–208 (1983)
Durgin, N.A., Lincoln, P., Mitchell, J.C., Scedrov, A.: Multiset rewriting and the complexity of bounded security protocols. J. Comput. Secur. 12(2), 247–311 (2004)
Enderton, H.B.: A Mathematical Introduction to Logic. Academic Press, Cambridge (1972)
Faella, M., Legay, A., Stoelinga, M.: Model checking quantitative linear time logic. Electr. Notes Theor. Comput. Sci. 220(3), 61–77 (2008)
Kanovich, M., Ban Kirigin, T., Nigam, V., Scedrov, A.: Bounded memory Dolev-Yao adversaries in collaborative systems. Inf. Comput. 238, 233–261 (2014)
Kanovich, M., Ban Kirigin, T., Nigam, V., Scedrov, A., Talcott, C.: Discrete vs. dense times in the analysis of cyber-physical security protocols. In: Principles of Security and Trust - 4th International Conference, POST, pp. 259–279 (2015)
Kanovich, M., Ban Kirigin, T., Nigam, V., Scedrov, A., Talcott, C.: Timed multiset rewriting and the verification of time-sensitive distributed systems. In: 14th International Conference on Formal Modeling and Analysis of Timed Systems (FORMATS) (2016)
Kanovich, M., Ban Kirigin, T., Nigam, V., Scedrov, A., Talcott, C.: On the complexity of verification of time-sensitive distributed systems: Technical report (2021). http://arxiv.org/abs/2105.03531
Kanovich, M., Ban Kirigin, T., Nigam, V., Scedrov, A., Talcott, C.L.: Timed multiset rewriting and the verification of time-sensitive distributed systems: Technical report (2016). http://arxiv.org/abs/1606.07886
Kanovich, M., Ban Kirigin, T., Nigam, V., Scedrov, A., Talcott, C.L.: Time, computational complexity, and probability in the analysis of distance-bounding protocols. J. Comput. Secur. 25(6), 585–630 (2017)
Kanovich, M., Ban Kirigin, T., Nigam, V., Scedrov, A., Talcott, C., Perovic, R.: A rewriting framework for activities subject to regulations. In: RTA, pp. 305–322 (2012)
Kanovich, M., Kirigin, T.B., Nigam, V., Scedrov, A., Talcott, C., Perovic, R.: A rewriting framework and logic for activities subject to regulations. Math. Struct. Comput. Sci. 27(3), 332–375 (2017)
Kanovich, M., Rowe, P., Scedrov, A.: Collaborative planning with confidentiality. J. Autom. Reasoning 46(3–4), 389–421 (2011)
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-time Syst. 2(4), 255–299 (1990)
Laroussinie, F., Schnoebelen, P., Turuani, M.: On the expressivity and complexity of quantitative branching-time temporal logics. Theor. Comput. Sci. 297(1–3), 297–315 (2003)
Lutz, C., Walther, D., Wolter, F.: Quantitative temporal logics: PSPACE and below. In: TIME, pp. 138–146 (2005)
Ölveczky, P.C., Meseguer, J.: Abstraction and completeness for real-time maude. Electr. Notes Theor. Comput. Sci. 176(4), 5–27 (2007)
Ölveczky, P.C., Meseguer, J.: The real-time maude tool. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 332–336. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78800-3_23
Ouaknine, J., Worrell, J.: Safety metric temporal logic is fully decidable. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 411–425. Springer, Heidelberg (2006). https://doi.org/10.1007/11691372_27
Papadimitriou, C.H.: Computational Complexity. Academic Internet Publishers, Cambridge (2007)
Urquiza, A., et al.: Resource and timing aspects of security protocols. J. Comput. Secur. 29(3), 299–340 (2021)
Urquiza, A., et al.: Resource-bounded intruders in denial of service attacks. In: 2019 IEEE 32nd Computer Security Foundations Symposium (CSF), pp. 382–396. IEEE (2019)
Acknowledgments
We thank the anonymous reviewers for their valuable comments and careful remarks, which have significantly improved the presentation of the paper. Ban Kirigin is supported in part by the Croatian Science Foundation under the project UIP-05-2017-9219. The work of Max Kanovich was partially supported by EPSRC Programme Grant EP/R006865/1: “Interface Reasoning for Interacting Systems (IRIS).” Nigam is partially supported by NRL grant N0017317-1-G002, and CNPq grant 303909/2018-8. Scedrov was partially supported by the U. S. Office of Naval Research under award numbers N00014-20-1-2635 and N00014-18-1-2618. Talcott was partially supported by the U. S. Office of Naval Research under award numbers N00014-15-1-2202 and N00014-20-1-2644, and NRL grant N0017317-1-G002.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kanovich, M., Kirigin, T.B., Nigam, V., Scedrov, A., Talcott, C. (2021). On the Complexity of Verification of Time-Sensitive Distributed Systems. In: Dougherty, D., Meseguer, J., Mödersheim, S.A., Rowe, P. (eds) Protocols, Strands, and Logic. Lecture Notes in Computer Science(), vol 13066. Springer, Cham. https://doi.org/10.1007/978-3-030-91631-2_14
Download citation
DOI: https://doi.org/10.1007/978-3-030-91631-2_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-91630-5
Online ISBN: 978-3-030-91631-2
eBook Packages: Computer ScienceComputer Science (R0)