Skip to main content
SpringerLink
Log in

Reachability Analysis Using Extremal Rates

  • Conference paper
  • First Online:
NASA Formal Methods (NFM 2015)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 9058))

Included in the following conference series:

  • 1533 Accesses

Abstract

General hybrid systems can be difficult to verify due to their generality. To reduce the complexity, one often specializes to hybrid systems where the complexity is more manageable. If one reduces the modeling formalism to ones where the continuous variables have a single rate, then it may be possible to use the methods of zones to find the reachable state space. Zones are a restricted class of polyhedra formed by considering the intersections of half-planes defined by two variable constraints. Due to their simplicity, zones have simpler, more efficient methods of manipulation than more general polyhedral classes, though they are less accurate. This paper extends the method of zones to labeled Petri net (LPN) models with continuous variables that evolve over a range of rates.

This material is based upon work supported by an ARCS Fellowship and the National Science Foundation (NSF) under Grant No. CCF-1117515 and CCF-1117660. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the NSF.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138, 3–34 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur, R., Courcoubeti, C., Henzinger, T.A., Ho, P.H.: Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.) Hybrid Systems. LNCS, vol. 736, pp. 209–229. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  3. Asarin, E., Dang, T., Maler, O.: The \(\mathbf{d/dt}\) tool for verification of hybrid systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 365–370. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. Bengtsson, J.E., Yi, W.: Timed Automata: Semantics, Algorithms and Tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) Lectures on Concurrency and Petri Nets. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  5. Cassez, F., Larsen, K.G.: The impressive power of stopwatches. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, p. 138. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  6. Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) Automatic Verification Methods for Finite State Systems. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  7. Fisher, A.N., Myers, C.J., Li, P.: Ranges of rates (2013) [Online; accessed 31-December-2014]. http://www.async.ece.utah.edu/~andrewf/ranges_of_rates.pdf

  8. Frehse, G., Le Guernic, C., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Frehse, G., Krogh, B., Rutenbar, R.: Verifying analog oscillator circuits using forward/backward abstraction refinement. In: DATE 2006 Proceedings of the Design, Automation and Test in Europe, vol. 1, p. 6, March 2006

    Google Scholar 

  10. Frehse, G.: Spaceex (2012) [Online; accessed 31-December-2012]. http://spaceex.imag.fr/documentation/publications

  11. Henzinger, T.A., Kopke, P.W., Puri, A., Varaiya, P.: What’s decidable about hybrid automata? In: Symposium on Theory of Computing, pp. 373–382. Association for Computing Machinery (1995). http://dl.acm.org/citation.cfm?id=225162

  12. Little, S., Seegmiller, N., Walter, D., Myers, C., Yoneda, T.: Verification of analog/mixed-signal circuits using labeled hybrid petri nets. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 30, 617–630 (2011)

    Article  Google Scholar 

  13. Little, S., Walter, D., Jones, K., Myers, C., Sen, A.: Analog/mixed-signal circuit verification using models generated from simulation traces. The Inernational Journal of Foundations of Computer Science 21(2), 191–210 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  14. Little, S.R.: Efficient modeling and verification of analog/mixed-signal circuits using labeled hybrid petri nets. Ph.D. thesis, University of Utah (2008)

    Google Scholar 

  15. Myers, C.: Asynchronous Circuit Design. John Wiley & Sons, July 2001

    Google Scholar 

  16. Puri, A., Borkar, V., Varaiya, P.: \(\epsilon \)-approximation of differential inclusions. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) HS 1995. LNCS, vol. 1066. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  17. Silva, B.I., Krogh, B.H.: Formal verification of hybrid systems using checkmate: A case study. American Control Conference 3, 1679–1683 (2000)

    Google Scholar 

  18. Yan, C., Greenstreet, M.: Faster projection based methods for circuit level verification. In: ASPDAC 2008 Design Automation Conference, Asia and South Pacific, pp. 410–415 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Utah, Salt Lake City, UT, 84112, USA

    Andrew N. Fisher & Chris J. Myers

  2. Texas A&M University, College Station, TX, 77843, USA

    Peng Li

Authors
  1. Andrew N. Fisher
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chris J. Myers
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrew N. Fisher .

Editor information

Editors and Affiliations

  1. Jet Propulsion Laboratory, Pasadena, California, USA

    Klaus Havelund

  2. Jet Propulsion Laboratory, Pasadena, California, USA

    Gerard Holzmann

  3. Jet Propulsion Laboratory, Pasadena, California, USA

    Rajeev Joshi

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Fisher, A.N., Myers, C.J., Li, P. (2015). Reachability Analysis Using Extremal Rates. In: Havelund, K., Holzmann, G., Joshi, R. (eds) NASA Formal Methods. NFM 2015. Lecture Notes in Computer Science(), vol 9058. Springer, Cham. https://doi.org/10.1007/978-3-319-17524-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-17524-9_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17523-2

  • Online ISBN: 978-3-319-17524-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation