Gate circuits in the algebra of transients

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

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Abstract

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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

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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

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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.
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