Temporal Properties of Self-Timed Rings

  • Anthony Winstanley
  • Mark Greenstreet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2144)


Various researchers have proposed using self-timed networks to generate and distribute clocks and other timing signals. We consider one of the simplest self-timed networks, a ring, and note that for timing applications, self-timed rings should maintain uniform spacing of events. In practice, all previous designs of which we are aware cluster events into bursts. In this paper, we describe a dynamical systems approach to verify the temporal properties of self-timed rings. With these methods, we can verify that a new design has the desired uniform spacing of events. The key to our methods is developing an appropriate model of the timing behaviour of our circuits. Our model is more accurate than the simplistic interval bounds of timed-automata techniques, while providing a higher level of abstraction than non-linear differential equation models such as SPICE. Evenly spaced and clustered event behaviours are distinguished by simple geometric features of our model.


Temporal Property Output Event Uniform Spacing Delay Model Input Event 
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  1. [AH99]
    Tod Amon and Henrik Hulgaard. Symbolic time separation of events. In Proceedings of the Fifth International Symposium on Advanced Research in Asynchronous Circuits and Systems, pages 83–93. IEEE, April 1999.Google Scholar
  2. [CS96]
    V. Chandromouli and K.A. Sakallah. Modeling the effects of temporal proximity of input transitions on gate propagation delay and transistion time. In Proceedings of the 33th ACM/IEEE Design Automation Conference, pages 617–622, June 1996.Google Scholar
  3. [DGV96]
    A. Deshpande, A. Gollu, and P.P. Varaiya. SHIFT, a formalism and programming language for dynamic networks of hybrid automata. In Proceedings of the Eigth Conference on Computer Aided Verification, pages 113–133, 1996.Google Scholar
  4. [DM+94]
    Florentin Dartu, Noel Menzes, et al. A gate delay model for high-speed CMOS circuits. In Proceedings of the 31th ACM/IEEE Design Automation Conference, pages 576–580, June 1994.Google Scholar
  5. [DP98]
    William J. Dally and John W. Poulton. Digital Systems Engineering. Cambridge University Press, 1998.Google Scholar
  6. [EFS98]
    Jo C. Ebergen, Scott Fairbanks, and Ivan E. Sutherland. Predicting performance of micropipelines using Charlie Diagrams. In Proceedings of the Fourth International Symposium on Advanced Research in Asynchronous Circuits and Systems, pages 238–246, April 1998.Google Scholar
  7. [GS90]
    Mark R. Greenstreet and Ken Steiglitz. Bubbles can make self-timed pipelines fast. Journal of VLSI and Signal Processing, 2(3):139–148, November 1990.Google Scholar
  8. [HBAB95]
    Henrik Hulgaard, Steven M. Burns, Tod Amon, and Gaetano Borriello. An algorithm for exact bounds on the time separation of events in concurrent systems. IEEE Transactions on Computers, 44(11):1306–1317, November 1995.Google Scholar
  9. [LPY97]
    Kim G. Larsen, Paul Petterson, and Wang Yi. UPPAAL: Status and developments. In Proceedings of the Ninth Conference on Computer Aided Verification, pages 456–459. Springer, June 1997. LNCS 1254.Google Scholar
  10. [Nag75]
    L.W. Nagel. SPICE2: a computer program to simulate semiconductor circuits. Technical Report ERL-M520, Electronics Research Laboratory, University of California, Berkeley, CA, May 1975.Google Scholar
  11. [SS93]
    Jens Sparsø and Jörgen Staunstrup. Delay-insensitive multi-ring structures. INTEGRATION, 15(3):313–340, October 1993.Google Scholar
  12. [Sut89]
    Ivan E. Sutherland. Micropipelines. Communications of the ACM, 32(6):720–738, June 1989. Turing Award lecture.Google Scholar
  13. [Thi91]
    Lothar Thiele. On the analysis and optimization of self-timed processor arrays. INTEGRATION, 12(2):167–187, December 1991.Google Scholar
  14. [Wil91]
    Ted E. Williams. Self-Timed Rings and their Application to Division. PhD thesis, Stanford University, May 1991.Google Scholar
  15. [XB97]
    Aiguo Xie and Peter A. Beerel. Symbolic techniques for performance analysis of timed systems based on average time separation of events. In Proc. International Symposium on Advanced Research in Asynchronous Circuits and Systems, pages 64–75. IEEE Computer Society Press, April 1997.Google Scholar
  16. [XKB99]
    Aiguo Xie, Sangyun Kim, and Peter A. Beerel. Bounding average time separations of events in stochastic timed Petri nets with choice. In Proc. International Symposium on Advanced Research in Asynchronous Circuits and Systems, pages 94–107, April 1999.Google Scholar
  17. [Yov97]
    Sergio Yovine. Kronos: A verification tool for real-time systems. Internation Journal of Software Tools for Technology Transfer, 1(1/2), October 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Anthony Winstanley
    • 1
  • Mark Greenstreet
    • 1
  1. 1.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada

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