Soft Computing

, Volume 22, Issue 4, pp 1139–1158 | Cite as

Compositionality for quantitative specifications

  • Uli Fahrenberg
  • Jan Křetínský
  • Axel Legay
  • Louis-Marie Traonouez
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  • 39 Downloads

Abstract

We provide a framework for compositional and iterative design and verification of systems with quantitative information, such as rewards, time or energy. It is based on disjunctive modal transition systems where we allow actions to bear various types of quantitative information. Throughout the design process, the actions can be further refined and the information made more precise. We show how to compute the results of standard operations on the systems, including the quotient (residual), which has not been previously considered for quantitative non-deterministic systems. Our quantitative framework has close connections to the modal nu-calculus and is compositional with respect to general notions of distances between systems and the standard operations.

Keywords

Compositionality Specification theory Disjunctive modal transition system Quantitative verification 

Notes

Acknowledgements

The J. Křetínský acknowledges support by the European Research Council (ERC) under Grant 267989 (QUAREM), by the Austrian Science Fund (FWF) under Grants S11402-N23 (RiSE) and Z211-N23 (Wittgenstein Award), the Czech Science Foundation Grant No. P202/12/G061, and the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) REA Grant No. 291734. The U. Fahrenberg, A. Legay, L.-M. Traonouez acknowledge support by ANR MALTHY, Grant No. ANR-13-INSE-0003 from the French National Research Foundation, and by the EU FP7 SENSATION Project, Grant No. 318490 (FP7-ICT-2011-8).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Irisa/Inria RennesRennesFrance
  2. 2.Technical University of MunichMunichGermany

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