TY - JOUR

T1 - Transforming probabilities with combinational logic

AU - Qian, Weikang

AU - Riedel, Marc D.

AU - Zhou, Hongchao

AU - Bruck, Jehoshua

PY - 2011/9/1

Y1 - 2011/9/1

N2 - Schemes for probabilistic computation can exploit physical sources to generate random values in the form of bit streams. Generally, each source has a fixed bias and so provides bits with a specific probability of being one. If many different probability values are required, it can be expensive to generate all of these directly from physical sources. This paper demonstrates novel techniques for synthesizing combinational logic that transforms source probabilities into different target probabilities. We consider three scenarios in terms of whether the source probabilities are specified and whether they can be duplicated. In the case that the source probabilities are not specified and can be duplicated, we provide a specific choice, the set 0.4, 0.5; we show how to synthesize logic that transforms probabilities from this set into arbitrary decimal probabilities. Further, we show that for any integer n ≥ 2, there exists a single probability that can be transformed into arbitrary base-n fractional probabilities. In the case that the source probabilities are specified and cannot be duplicated, we provide two methods for synthesizing logic to transform them into target probabilities. In the case that the source probabilities are not specified, but once chosen cannot be duplicated, we provide an optimal choice.

AB - Schemes for probabilistic computation can exploit physical sources to generate random values in the form of bit streams. Generally, each source has a fixed bias and so provides bits with a specific probability of being one. If many different probability values are required, it can be expensive to generate all of these directly from physical sources. This paper demonstrates novel techniques for synthesizing combinational logic that transforms source probabilities into different target probabilities. We consider three scenarios in terms of whether the source probabilities are specified and whether they can be duplicated. In the case that the source probabilities are not specified and can be duplicated, we provide a specific choice, the set 0.4, 0.5; we show how to synthesize logic that transforms probabilities from this set into arbitrary decimal probabilities. Further, we show that for any integer n ≥ 2, there exists a single probability that can be transformed into arbitrary base-n fractional probabilities. In the case that the source probabilities are specified and cannot be duplicated, we provide two methods for synthesizing logic to transform them into target probabilities. In the case that the source probabilities are not specified, but once chosen cannot be duplicated, we provide an optimal choice.

KW - Logic synthesis

KW - probabilistic logic

KW - probabilistic signals

KW - random bit streams

KW - stochastic bit streams

UR - http://www.scopus.com/inward/record.url?scp=80052062709&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80052062709&partnerID=8YFLogxK

U2 - 10.1109/TCAD.2011.2144630

DO - 10.1109/TCAD.2011.2144630

M3 - Article

AN - SCOPUS:80052062709

VL - 30

SP - 1279

EP - 1292

JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

SN - 0278-0070

IS - 9

M1 - 5989992

ER -