Geodesic
A stochastic model of a digit transfer by computing
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 417-423 
L. Ya. Savelev; S. V. Balakin. A stochastic model of a digit transfer by computing. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 4, pp. 417-423. http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a6/
@article{SJVM_2012_15_4_a6,
     author = {L. Ya. Savelev and S. V. Balakin},
     title = {A stochastic model of a~digit transfer by computing},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {417--423},
     year = {2012},
     volume = {15},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a6/}
}
TY  - JOUR
AU  - L. Ya. Savelev
AU  - S. V. Balakin
TI  - A stochastic model of a digit transfer by computing
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2012
SP  - 417
EP  - 423
VL  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a6/
LA  - ru
ID  - SJVM_2012_15_4_a6
ER  - 
%0 Journal Article
%A L. Ya. Savelev
%A S. V. Balakin
%T A stochastic model of a digit transfer by computing
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2012
%P 417-423
%V 15
%N 4
%U http://geodesic.mathdoc.fr/item/SJVM_2012_15_4_a6/
%G ru
%F SJVM_2012_15_4_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper describes a stochastic model of the digit transfer. The main characteristics of the transfer process are the number of transfers, a number of groups of consecutive transfers and a maximum number of consecutive transfers. Two binary numbers with a digit transfer form a triplet, and a sequence of these triplets generates a Markov chain. In our model the above-mentioned characteristics can be described by functionals on trajectories of this chain. They are: the number of events, the number of runs of these events and a maximum run length. These characteristics can be efficiently used for estimation of a computation speed.

[1] Rabai Zh. M., Chandrakasan A., Nikolich B., “Proektirovanie arifmeticheskikh blokov: Summator”, Tsifrovye integralnye skhemy. Metodologiya proektirovaniya, Per. s angl., 2-e izd., Vilyams, M., 2007

[2] Preet Pa Singh R., Kumar P., Singh B., “Performance analysis of 32-bit array multiplier with a carry save adder and with a carry-look-ahead adder”, International J. of Recent Trends in Engineering, 2:6 (2009), 83–86

[3] Ercegovac M. D., Lang T., Digital Arithmetic, Morgan Daufmann, San Francisco, 2004

[4] Ugryumov E. P., Tsifrovaya skhemotekhnika, BKhV-Peterburg, SPb., 2001

[5] Khmelnik S. I., Kodirovanie kompleksnykh chisel i vektorov. Teoriya, apparatura, modelirovanie, Mathematics in Computers, Israel; Lulu Inc., USA, 2006, (ID 560836)

[6] Kemeni Dzh., Snell Dzh., Konechnye tsepi Markova, Nauka, M., 1978

[7] Bremaud P., Markov Chains. Gibbs Filds. Monte Carlo Simulations, and Queues, Springer, 1998 | MR

[8] Savelev L. Ya., Balakin S. V., “Sovmestnoe raspredelenie chisla edinits i chisla 1-serii v dvoichnoi markovskoi posledovatelnosti”, Diskretnaya matematika, 16:3 (2004), 43–62 | DOI | MR | Zbl

[9] Balakin S. V., “Raspredelenie maksimuma dlin serii v markovskoi tsepi”, Obozrenie prikladnoi i promyshlennoi matematiki, 17:4 (2010), 531–532

[10] Savelev L. Ya., Balakin S. V., “Kombinatornoe vychislenie momentov kharakteristik serii v troichnykh markovskikh posledovatelnostyakh”, Diskretnaya matematika, 23:2 (2011), 76–92 | DOI | MR

[11] Savelev L. Ya., “Dlinnye serii v markovskikh posledovatelnostyakh”, Predelnye teoremy teorii veroyatnostei, 5, 1985, 137–144 | MR