Gate circuits in the algebra of transients

Janusz Brzozowski; Mihaela Gheorghiu

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 39, Issue: 1, page 67-91
  • ISSN: 0988-3754

Abstract

top

We study simulation of gate circuits in the infinite algebra of transients recently introduced by Brzozowski and Ésik. A transient is a word consisting of alternating 0s and 1s; it represents a changing signal. In the algebra of transients, gates process transients instead of 0s and 1s. Simulation in this algebra is capable of counting signal changes and detecting hazards. We study two simulation algorithms: a general one that works with any initial state, and a special one that applies only if the initial state is stable. We show that the two algorithms agree in the stable case. We also show that the general algorithm is insensitive to the removal of state variables that are not feedback variables. We prove the sufficiency of simulation: all signal changes occurring in binary analysis are predicted by the general algorithm. Finally, we show that simulation can be more pessimistic than binary analysis, if wire delays are not taken into account. We propose a circuit model that we conjecture to be sufficient for proving the equivalence of simulation and binary analysis for feedback-free circuits.


How to cite

top

Brzozowski, Janusz, and Gheorghiu, Mihaela. "Gate circuits in the algebra of transients." RAIRO - Theoretical Informatics and Applications 39.1 (2010): 67-91. <http://eudml.org/doc/92766>.

@article{Brzozowski2010,
abstract = {
We study simulation of gate circuits in the infinite algebra of transients recently introduced by Brzozowski and Ésik. A transient is a word consisting of alternating 0s and 1s; it represents a changing signal. In the algebra of transients, gates process transients instead of 0s and 1s. Simulation in this algebra is capable of counting signal changes and detecting hazards. We study two simulation algorithms: a general one that works with any initial state, and a special one that applies only if the initial state is stable. We show that the two algorithms agree in the stable case. We also show that the general algorithm is insensitive to the removal of state variables that are not feedback variables. We prove the sufficiency of simulation: all signal changes occurring in binary analysis are predicted by the general algorithm. Finally, we show that simulation can be more pessimistic than binary analysis, if wire delays are not taken into account. We propose a circuit model that we conjecture to be sufficient for proving the equivalence of simulation and binary analysis for feedback-free circuits.
},
author = {Brzozowski, Janusz, Gheorghiu, Mihaela},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Algebra; digital circuit; hazard detection; signal changes; simulation; transient.; gate circuits; feedback-free circuits},
language = {eng},
month = {3},
number = {1},
pages = {67-91},
publisher = {EDP Sciences},
title = {Gate circuits in the algebra of transients},
url = {http://eudml.org/doc/92766},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Brzozowski, Janusz
AU - Gheorghiu, Mihaela
TI - Gate circuits in the algebra of transients
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 39
IS - 1
SP - 67
EP - 91
AB - 
We study simulation of gate circuits in the infinite algebra of transients recently introduced by Brzozowski and Ésik. A transient is a word consisting of alternating 0s and 1s; it represents a changing signal. In the algebra of transients, gates process transients instead of 0s and 1s. Simulation in this algebra is capable of counting signal changes and detecting hazards. We study two simulation algorithms: a general one that works with any initial state, and a special one that applies only if the initial state is stable. We show that the two algorithms agree in the stable case. We also show that the general algorithm is insensitive to the removal of state variables that are not feedback variables. We prove the sufficiency of simulation: all signal changes occurring in binary analysis are predicted by the general algorithm. Finally, we show that simulation can be more pessimistic than binary analysis, if wire delays are not taken into account. We propose a circuit model that we conjecture to be sufficient for proving the equivalence of simulation and binary analysis for feedback-free circuits.

LA - eng
KW - Algebra; digital circuit; hazard detection; signal changes; simulation; transient.; gate circuits; feedback-free circuits
UR - http://eudml.org/doc/92766
ER -

References

top
  1. Ann. Symp. Asynchronous Circuits and Systems, Proc. 9th (ASYNC '03), IEEE Comp. Soc. (2003).  
  2. J.A. Brzozowski and Z. Ésik, Hazard algebras. Formal Methods in System Design23 (2003) 223–256.  Zbl1073.68883
  3. J.A. Brzozowski, Z. Ésik and Y. Iland, Algebras for hazard detection. Beyond Two: Theory and Applications of Multiple-Valued Logic, edited by M. Fitting and E. Orłowska. Physica-Verlag (2003) 3–24.  Zbl1046.94021
  4. J.A. Brzozowski and M. Gheorghiu, Simulation of gate circuits in the algebra of transients. Implementation and Application of Automata. Lect. Notes Comput. Sci.2608 (2003) 57–66.  Zbl1033.94568
  5. J.A. Brzozowski and C.-J.H. Seger, Asynchronous circuits. Springer-Verlag (1995).  Zbl0879.94040
  6. J.A. Brzozowski and C.-J.H. Seger, A characterization of ternary simulation of gate networks. IEEE Trans. Comp.C-36 (1987) 1318–1327.  Zbl0641.94030
  7. J.A. Brzozowski and M. Yoeli, On a ternary model of gate networks. IEEE Trans. Comp.C-28 (1979) 178–183.  Zbl0408.94023
  8. E.B. Eichelberger, Hazard detection in combinational and sequential circuits. IBM J. Res. Dev.9 (1965) 90–99.  Zbl0132.37106
  9. J.D. Garside, AMULET3 revealed, in Proc. 5th Ann. Symp. Asynchronous Circuits and Systems (ASYNC '99), IEEE Comp. Soc. (1999) 51–59.  
  10. M. Gheorghiu, Circuit simulation using a hazard algebra. MMath Thesis, Department of Computer Science, University of Waterloo, Waterloo, ON, Canada (2001).  
  11. M. Gheorghiu and J.A. Brzozowski, Simulation of feedback-free circuits in the algebra of transients. Int. J. Found. Comput. Sci.14 (2003) 1033–1054.  Zbl1101.68652
  12. J. Kessels and P. Marston, Designing asynchronous standby circuits for a low-power pager, in Proc. 3rd Ann. Symp. Asynchronous Circuits and Systems (ASYNC '97), IEEE Comp. Soc. (1997) 268–278.  
  13. E.J. McCluskey, Transients in combinational logic circuits. Redundancy techniques for computing systems, edited by R.H. Wilcox and W.C. Mann. Spartan Books (1962) 9–46.  
  14. D.E. Muller and W.C. Bartky, A theory of asynchronous circuits, in Proc. Int. Symp. on Theory of Switching, Annals of Comp. Lab. Harvard University 29 (1959) 204–243.  Zbl0171.37902
  15. C.-J.H. Seger and J.A. Brzozowski, Generalized ternary simulation of sequential circuits. Theor. Inf. Appl.28 (1994) 159–186.  Zbl0879.94040
  16. I.E. Sutherland and J. Ebergen, Computers without Clocks. Sci. Amer.287 (2002) 62–69.  
  17. S.H. Unger, Asynchronous sequential switching circuits. John Wiley & Sons (1969).  

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.