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Quantitative Abstractions for Collective Adaptive Systems

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Formal Methods for the Quantitative Evaluation of Collective Adaptive Systems (SFM 2016)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9700))

Abstract

Collective adaptive systems (CAS) consist of a large number of possibly heterogeneous entities evolving according to local interactions that may operate across multiple scales in time and space. The adaptation to changes in the environment, as well as the highly dispersed decision-making process, often leads to emergent behaviour that cannot be understood by simply analysing the objectives, properties, and dynamics of the individual entities in isolation.

As with most complex systems, modelling is a phase of crucial importance for the design of new CAS or the understanding of existing ones. Elsewhere in this volume the typical workflow of formal modelling, analysis, and evaluation of a CAS has been illustrated in detail. In this chapter we treat the problem of efficiently analysing large-scale CAS for quantitative properties. We review algorithms to automatically reduce the dimensionality of a CAS model preserving modeller-defined state variables, with focus on descriptions based on systems of ordinary differential equations. We illustrate the theory in a tutorial fashion, with running examples and a number of more substantial case studies ranging from crowd dynamics, epidemiology and biological systems.

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Notes

  1. 1.

    Throughout the paper we will work with autonomous ODE systems, which are not explicitly dependent on time.

  2. 2.

    Note that \([s_i]\cdot [s_i]\) should actually be \([s_i]\cdot ([s_i] - 1)\), since an individual cannot meet itself. However, this is irrelevant for large populations, and hence, as for existing ODE-based semantics in the biological context [78], we approximate it to \([s_i]\cdot [s_i]\).

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Acknowledgement

This work was partially supported by the EU project QUANTICOL, 600708. The authors thank Luca Cardelli and Max Tschaikowski who co-authored the papers [19–21] used as background material in this chapter.

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  1. IMT School for Advanced Studies Lucca, Lucca, Italy

    Andrea Vandin & Mirco Tribastone

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  1. Andrea Vandin
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    Marco Bernardo

  2. IMT - School for Advanced Studies, Lucca, Italy

    Rocco De Nicola

  3. School of Informatics, University of Edinburgh, Edinburgh, United Kingdom

    Jane Hillston

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Vandin, A., Tribastone, M. (2016). Quantitative Abstractions for Collective Adaptive Systems. In: Bernardo, M., De Nicola, R., Hillston, J. (eds) Formal Methods for the Quantitative Evaluation of Collective Adaptive Systems. SFM 2016. Lecture Notes in Computer Science(), vol 9700. Springer, Cham. https://doi.org/10.1007/978-3-319-34096-8_7

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