On Temporal Logic and Signal Processing

  • Alexandre Donzé
  • Oded Maler
  • Ezio Bartocci
  • Dejan Nickovic
  • Radu Grosu
  • Scott Smolka
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7561)


We present Time-Frequency Logic (TFL), a new specification formalism for real-valued signals that combines temporal logic properties in the time domain with frequency-domain properties. We provide a property checking framework for this formalism and illustrate its expressive power in defining and recognizing properties of musical pieces. Like hybrid automata and their analysis techniques, the TFL formalism is a contribution to a unified systems theory for hybrid systems.


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  1. 1.
    Benveniste, A., Le Guernic, P., Jacquemot, C.: Synchronous programming with events and relations: the signal language and its semantics. Sci. Comput. Program. 16(2), 103–149 (1991)CrossRefMATHGoogle Scholar
  2. 2.
    Caspi, P., Pilaud, D., Halbwachs, N., Plaice, J.: Lustre: A declarative language for programming synchronous systems. In: POPL, pp. 178–188 (1987)Google Scholar
  3. 3.
    Chakarov, A., Sankaranarayanan, S., Fainekos, G.: Combining Time and Frequency Domain Specifications for Periodic Signals. In: Khurshid, S., Sen, K. (eds.) RV 2011. LNCS, vol. 7186, pp. 294–309. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    d’Angelo, B., Sankaranarayanan, S., Sánchez, C., Robinson, W., Finkbeiner, B., Sipma, H.B., Mehrotra, S., Manna, Z.: Lola: Runtime monitoring of synchronous systems. In: TIME, pp. 166–174. IEEE (2005)Google Scholar
  5. 5.
    Donzé, A.: Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 167–170. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Donzé, A., Fanchon, E., Gattepaille, L.M., Maler, O., Tracqui, P.: Robustness analysis and behavior discrimination in enzymatic reaction networks. PLoS One 6(9) (2011)Google Scholar
  7. 7.
    Donzé, A., Maler, O.: Robust Satisfaction of Temporal Logic over Real-Valued Signals. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 92–106. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  8. 8.
    Fourier, J.B.G.: Theórie analytique de la chaleur. Gauthier-Villars et fils (1888)Google Scholar
  9. 9.
    Frigo, M., Johnson, S.G.: The fastest Fourier transform in the west. Technical Report MIT-LCS-TR-728, Massachusetts Institute of Technology (September 1997)Google Scholar
  10. 10.
    Gabor, D.: Theory of communication. part 1: The analysis of information electrical engineers. Journal of the IEEE - Part III: Radio and Communication Engineering 93(26), 429–441 (1946)Google Scholar
  11. 11.
    Giorgidze, G., Nilsson, H.: Switched-On Yampa. In: Hudak, P., Warren, D.S. (eds.) PADL 2008. LNCS, vol. 4902, pp. 282–298. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Grosu, R., Bartocci, E., Corradini, F., Entcheva, E., Smolka, S.A., Wasilewska, A.: Learning and Detecting Emergent Behavior in Networks of Cardiac Myocytes. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 229–243. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Grosu, R., Smolka, S., Corradini, F., Wasilewska, A., Entcheva, E., Bartocci, E.: Learning and detecting emergent behavior in networks of cardiac myocytes. Communications of the ACM 52(3), 1–10 (2009)CrossRefGoogle Scholar
  14. 14.
    Harel, D., Pnueli, A.: On the development of reactive systems. In: Apt, K.R. (ed.) Logics and Models of Concurrent Systems. NATO ASI Series, pp. 477–498. Springer (1985)Google Scholar
  15. 15.
    Hubbard, B.B.: The world according to wavelets. The story of a mathematical technique in the making, 2nd edn. CRC Press (2010)Google Scholar
  16. 16.
    Hudak, P., Courtney, A., Nilsson, H., Peterson, J.: Arrows, Robots, and Functional Reactive Programming. In: Jeuring, J., Jones, S.L.P. (eds.) AFP 2002. LNCS, vol. 2638, pp. 159–187. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  17. 17.
    Jones, K., Konrad, V., Nickovic, D.: Analog property checkers: a DDR2 case study. Formal Methods in System Design (2009)Google Scholar
  18. 18.
    Kesten, Y., Pnueli, A.: A compositional approach to CTL* verification. Theor. Comput. Sci. 331(2-3), 397–428 (2005)CrossRefMathSciNetMATHGoogle Scholar
  19. 19.
    Maler, O., Nickovic, D.: Monitoring Temporal Properties of Continuous Signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  20. 20.
    Maler, O., Nickovic, D., Pnueli, A.: From MITL to Timed Automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 274–289. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    Maler, O., Nickovic, D., Pnueli, A.: Checking Temporal Properties of Discrete, Timed and Continuous Behaviors. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 475–505. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  22. 22.
    Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press (2008)Google Scholar
  23. 23.
    Michel, M.: Composition of temporal operators. Logique et Analyse 110-111, 137–152 (1985)Google Scholar
  24. 24.
    Mukherjee, S., Dasgupta, P., Mukhopadhyay, S.: Auxiliary specifications for context-sensitive monitoring of AMS assertions. IEEE Transactions on CAD 30(10), 1446–1457 (2011)CrossRefGoogle Scholar
  25. 25.
    Nickovic, D., Maler, O.: AMT: A Property-Based Monitoring Tool for Analog Systems. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 304–319. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  26. 26.
    Pembeci, I., Nilsson, H., Hager, G.: Functional reactive robotics: an exercise in principled integration of domain-specific languages. In: PADP, pp. 168–179. ACM (2002)Google Scholar
  27. 27.
    Pino, J.L., Ha, S., Lee, E.A., Buck, J.T.: Software synthesis for DSP using Ptolemy. VLSI Signal Processing 9(1-2), 7–21 (1995)CrossRefGoogle Scholar
  28. 28.
    Pnueli, A.: The temporal logic of programs. In: Proc. 18th Annual Symposium on Foundations of Computer Science (FOCS), pp. 46–57 (1977)Google Scholar
  29. 29.
    Pnueli, A.: The Temporal Semantics of Concurrent Programs. Theoretical Computer Science 13, 45–60 (1981)CrossRefMathSciNetMATHGoogle Scholar
  30. 30.
    Pnueli, A., Zaks, A.: On the Merits of Temporal Testers. In: Grumberg, O., Veith, H. (eds.) 25 Years of Model Checking. LNCS, vol. 5000, pp. 172–195. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  31. 31.
    Prior, A.N.: Past, Present, Future, Oxford (1969)Google Scholar
  32. 32.
    Rescher, N., Urquhart, A.: Temporal Logic. Springer (1971)Google Scholar
  33. 33.
    Vardi, M.Y.: From Philosophical to Industrial Logics. In: Ramanujam, R., Sarukkai, S. (eds.) ICLA 2009. LNCS (LNAI), vol. 5378, pp. 89–115. Springer, Heidelberg (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alexandre Donzé
    • 1
  • Oded Maler
    • 2
  • Ezio Bartocci
    • 4
  • Dejan Nickovic
    • 3
  • Radu Grosu
    • 4
  • Scott Smolka
    • 5
  1. 1.EECS DepartmentUniversity of CaliforniaBerkeleyUSA
  2. 2.VerimagUniversité Joseph Fourier/CNRSGièresFrance
  3. 3.Austrian Institute of TechnologyViennaAustria
  4. 4.Department of Computer EngineeringVienna, University of TechnologyAustria
  5. 5.Department of Computer ScienceStony Brook UniversityUSA

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