Abstract
Software is increasingly embedded in a variety of physical contexts. This imposes new requirements on tools that support the design and analysis of systems. For instance, modeling embedded and cyber-physical systems needs to blend discrete mathematics, which is suitable for modeling digital components, with continuous mathematics, used for modeling physical components. This blending of continuous and discrete creates challenges that are absent when the discrete or the continuous setting are considered in isolation. We consider robustness, that is, the ability of an analysis of a model to cope with small amounts of imprecision in the model. Formally, we identify analyses with monotonic maps between complete lattices (a mathematical framework used for abstract interpretation and static analysis) and define robustness for monotonic maps between complete lattices of closed subsets of a metric space.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This does not exclude the possibility of using imprecise (aka loose) specifications.
- 2.
Representing a real with a float, as done in traditional numerical methods, means that the imprecision in computations is either ignored or is tracked manually.
References
Alur, R., et al.: The algorithmic analysis of hybrid systems. Theor. Comput. Sci. 138(1), 3–34 (1995)
Asperti, A., Longo, G.: Categories, Types and Scructures: An Introduction to Category Theory for the Working Computer Scientist. MIT Press, Cambridge (1991)
Awodey, S.: Category Theory. Oxford University Press, Oxford (2010)
Conway, J.B.: A Course in Functional Analysis, 2nd edn. Springer, New York (1990)
Cousot, P., Cousot, R.: Abstract interpretation frameworks. J. Logic Comput. 2(4), 511–547 (1992)
Cuijpers, P.J.L., Reniers, M.A.: Topological (bi-) simulation. Electron. Notes Theor. Comput. Sci. 100, 49–64 (2004)
Fränzle, M.: Analysis of hybrid systems: an ounce of realism can save an infinity of states. In: Flum, J., Rodriguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 126–139. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48168-0_10
Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M.W., Scott, D.S.: Encycloedia of mathematics and its applications. Continuous Lattices and Domains, vol. 93. Cambridge University Press, Cambridge (2003)
Goebel, R., Sanfelice, R.G., Teel, A.: Hybrid dynamical systems. IEEE Control Syst. 29(2), 28–93 (2009)
Kelley, J.L.: General Topology. Springer, Berlin (1975)
Kong, S., Gao, S., Chen, W., Clarke, E.: dReach: \({\delta }\)-reachability analysis for hybrid systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 200–205. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_15
Larsen, K.G., Steffen, B., Weise, C.: Continuous modeling of real-time and hybrid systems: from concepts to tools. Int. J. Softw. Tools Technol. Transfer 1(1–2), 64–85 (1997)
Moggi, E., Farjudian, A., Duracz, A., Taha, W.: Safe & robust reachability analysis of hybrid systems. Theor. Comput. Sci. 747C, 75–99 (2018). https://doi.org/10.1016/j.tcs.2018.06.020
Moore, R.E.: Interval Analysis. Prentice-Hall, New Jersey (1966)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Moggi, E., Farjudian, A., Taha, W. (2019). System Analysis and Robustness. In: Margaria, T., Graf, S., Larsen, K. (eds) Models, Mindsets, Meta: The What, the How, and the Why Not?. Lecture Notes in Computer Science(), vol 11200. Springer, Cham. https://doi.org/10.1007/978-3-030-22348-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-22348-9_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-22347-2
Online ISBN: 978-3-030-22348-9
eBook Packages: Computer ScienceComputer Science (R0)