کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1155375 | 1378664 | 2016 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Volatility of Boolean functions
ترجمه فارسی عنوان
نوسانات توابع بولی
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
We study the volatility of the output of a Boolean function when the input bits undergo a natural dynamics. For n=1,2,â¦, let fn:{0,1}mnâ{0,1} be a Boolean function and X(n)(t)=(X1(t),â¦,Xmn(t))tâ[0,â) be a vector of i.i.d. stationary continuous time Markov chains on {0,1} that jump from 0 to 1 with rate pnâ[0,1] and from 1 to 0 with rate qn=1âpn. Our object of study will be Cn which is the number of state changes of fn(X(n)(t)) as a function of t during [0,1]. We say that the family {fn}nâ¥1 is volatile if Cnââ in distribution as nââ and say that {fn}nâ¥1 is tame if {Cn}nâ¥1 is tight. We study these concepts in and of themselves as well as investigate their relationship with the recent notions of noise sensitivity and noise stability. In addition, we study the question of lameness which means that P(Cn=0)â1 as nââ. Finally, we investigate these properties for the majority function, iterated 3-majority, the AND/OR function on the binary tree and percolation on certain trees in various regimes.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 126, Issue 10, October 2016, Pages 2956-2975
Journal: Stochastic Processes and their Applications - Volume 126, Issue 10, October 2016, Pages 2956-2975
نویسندگان
Johan Jonasson, Jeffrey E. Steif,