# 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

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topBrzozowski, 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

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- 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.
- 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
- C.-J.H. Seger and J.A. Brzozowski, Generalized ternary simulation of sequential circuits. Theor. Inf. Appl.28 (1994) 159–186. Zbl0879.94040
- I.E. Sutherland and J. Ebergen, Computers without Clocks. Sci. Amer.287 (2002) 62–69.
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