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Formal Verification for Nonlinear Analog Systems: Approaches to Model and Equivalence Checking

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Advanced Formal Verification

Abstract

In this contribution, we present equivalence and model checking methods for nonlinear analog systems. Both approaches are based one the system’s nonlinear state space description. The equivalence checker computes a nonlinear transformation of the state space descriptions into a canonical form. Thus, the input/output behavior of the specifying and the target system can be compared independently of the different state representations. The model checking approach uses an automatic state space subdivision method to transfer the continuous state space into a discrete model retaining the essential analog dynamics. The analog system properties are described in an extended CTL language. Experimental results show the feasibility of both approaches.

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References

  1. R. Alur, T.A. Henzinger, G. Lafferriere, and G.J. Pappas. Discrete abstractions of hybrid systems. Proceedings of IEEE, (88):971–984, 2000.

    Google Scholar 

  2. K.J. Antreich, H.E. Graeb, and C.U. Wieser. Circuit analysis and optimization driven by worst-case distances. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 13(1):57–71, 1994.

    Article  Google Scholar 

  3. E. Asarin, O. Bournez, T. Dang, and O. Maler. Approximate reachability analysis of piecewise-linear dynamical systems. HSCC’ 00: Hybrid Systems: Computation and Control, LNCS, pages 76–90, 2000.

    Google Scholar 

  4. P.N. Brown, A.C. Hindmarsh, and R.P. Linda. Consistent initial condition calculation for differential-algebraic systems. SIAM Journal on Scientific Computing, 19(5):1495–1512, 1998.

    Article  MathSciNet  Google Scholar 

  5. F.H. Bursal and B.H. Tongue. A new method of nonlinear system identification using interpolated cell mapping. ACC’ 92: American Control Conference, 4:3160–3164, 1992.

    Google Scholar 

  6. E.M. Clarke and E.A. Emerson. Design and synthesis of synchronisation skeletons using branching time temporal logic. Lecture Notes in Computer Science, Springer-Verlag, 131, 1981.

    Google Scholar 

  7. T. Dang and O. Maler. Reachability analysis via face lifting. HSCC’ 98: Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, pages 96–109, 1998.

    Google Scholar 

  8. M. Dellnitz, G. Froyland, and O. Junge. The algorithms behind gaio — set oriented numerical methods for dynamical systems. Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems (eds. B. Fiedler), Springer, pages 145–174, 2001.

    Google Scholar 

  9. A. Dharchoudhury and S.M. Kang. Worst-case analysis and optimization of VLSI circuit performances. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 14(4):481–492, 1995.

    Article  Google Scholar 

  10. P. Van. Dooren. The computation of Kronecker’s canonical form of a singular pencil. Journal on Linear Algebra and its Applications, 27:103–140, 1979.

    MATH  Google Scholar 

  11. D. Estévez-Schwarz. Consistent initialization for index-2 differential algebraic equations and its application to circuit simulation. Dissertation, Humboldt-Universität Berlin, 2000.

    Google Scholar 

  12. P. Feldmann and R.W. Freund. Effcient linear circuits analysis by pade approximation via the lanczos process. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 14(5):639–649, 1995.

    Article  Google Scholar 

  13. L. Fortuna, G. Nunnari, and A. Gallo. Model order reduction techniques with applications in electrical engineering. Springer-Verlag, Berlin, 1992.

    Google Scholar 

  14. C.W. Gear. Differential algebraic equations, indices, and integral algebraic equations. SIAM Journal on Numerical Analysis, 27(6):1527–1534, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  15. M. Günther and U. Feldmann. The DAE-index in electric circuit simulation. Mathematisches Institut, Technische Universität München, 1993.

    Google Scholar 

  16. W. Hartong, L. Hedrich, and E. Barke. Model checking algorithms for analog verification. DAC’ 02: Design Automation Conference, pages 542–547, 2002.

    Google Scholar 

  17. W. Hartong, L. Hedrich, and E. Barke. Ondiscrete modeling and model checking for nonlinear analog systems. CAV’ 02: International Conference on Computer-Aided Verification, LNCS, 2404:401–413, 2002.

    Google Scholar 

  18. L. Hedrich and E. Barke. A formal approach to nonlinear analog circuit verification. ICCAD’ 95: International Conference on Computer Aided Design, pages 123–127, 1995.

    Google Scholar 

  19. L. Hedrich and E. Barke. A formal approach to verification of linear analog circuits with parameter tolerances. DATE’ 98: Design, Automation and Test in Europe, pages 649–654, 1998.

    Google Scholar 

  20. L. Hedrich and W. Hartong. Approaches to formal verification of analog circuits. Low-Power Design Techniques and CAD Tools for Analog and RF Intergrated Circuits, Wambacq, P., eds., Kluwer Academic Publishers, Boston, 2001.

    Google Scholar 

  21. T.A. Henzinger and P.-H. Ho. Algorithmic analysis of nonlinear hybrid systems. CAV’ 95: International Conference on Computer-Aided Verification, LNCS, 939(7):225–238, 1995.

    Google Scholar 

  22. T.A. Henzinger, P-H. Ho, and H. Wong-Toi. Hytech: A model checker for hybrid systems. Lecture Notes in Computer Science, Springer-Verlag, pages 460–463, 1997.

    Google Scholar 

  23. C.W. Ho, A.E. Ruehli, and P.A. Brennan. The modified nodal approach to network analysis. IEEE Transactions on Circuits and Systems, 22(6):504–509, 1975.

    Google Scholar 

  24. T. Kropf. Introduction to formal hardware verification. Springer-Verlag, Berlin, Heidelberg, 1999.

    Google Scholar 

  25. R.P. Kurshan and K.L. McMillan. Analysis of digital circuits through symbolic reduction. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 10(11):1356–1371, 1991.

    Article  Google Scholar 

  26. F. Laroussinie and P. Schnoebelen. Specification in CTL+past for verification in CTL. Information and Computation, 156(1/2):236–263, 2000.

    MathSciNet  Google Scholar 

  27. R. März. Numerical methods for differential algebraic equations. Acta Numerica, pages 141–198, 1991.

    Google Scholar 

  28. W. Mathis. Theorie nichtlinearer Netzwerke. Springer-Verlag, Berlin, 1987. (German).

    Google Scholar 

  29. K.L. McMillian. Symbolic model checking. Kluwer Academic Publishers, Boston, 1993.

    Google Scholar 

  30. S. Natarajan. A systematic method for obtaining state equations using MNA. IEE Proceedings G, 138(3):341–346, 1991.

    MathSciNet  Google Scholar 

  31. L. Petzold. Differential/algebraic equations are not ODE’s. JSIAM, 3(3):367–384, 1982.

    MathSciNet  MATH  Google Scholar 

  32. A. Puri and P. Varaiya. Decidability of hybrid systems with rectangular differential inclusions. CAV’ 94: International Conference on Computer-Aided Verification, LNCS, pages 95–104, 1994.

    Google Scholar 

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Hartong, W., Klausen, R., Hedrich, L. (2004). Formal Verification for Nonlinear Analog Systems: Approaches to Model and Equivalence Checking. In: Drechsler, R. (eds) Advanced Formal Verification. Springer, Boston, MA. https://doi.org/10.1007/1-4020-2530-0_6

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  • DOI: https://doi.org/10.1007/1-4020-2530-0_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4020-7721-0

  • Online ISBN: 978-1-4020-2530-3

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