A DNC function that computes no effectively bi-immune set
نویسنده
چکیده
In Diagonally Non-Computable Functions and Bi-Immunity [2], Carl Jockusch and Andrew Lewis-Pye proved that every DNC function computes a bi-immune set. They asked whether every DNC function computes an effectively bi-immune set. We construct a DNC function that computes no effectively bi-immune set, thereby answering their question in the negative.
منابع مشابه
Diagonally non-computable functions and fireworks
A set C of reals is said to be negligible if there is no probabilistic algorithm which generates a member of C with positive probability. Various classes have been proven to be negligible, for example the Turing upper-cone of a non-computable real, the class of coherent completions of Peano Arithmetic or the class of reals of minimal degrees. One class of particular interest in the study of neg...
متن کاملDiagonally non-computable functions and bi-immunity
We prove that every diagonally noncomputable function computes a set A which is bi-immune, meaning that neither A nor its complement has an infinite computably enumerable subset.
متن کاملEffective Bi-immunity and Randomness
We study the relationship between randomness and effective biimmunity. Greenberg and Miller have shown that for any oracle X, there are arbitrarily slow-growing DNR functions relative to X that compute no MartinLöf random set. We show that the same holds when Martin-Löf randomness is replaced with effective bi-immunity. It follows that there are sequences of effective Hausdorff dimension 1 that...
متن کاملپروتکل کارا برای جمع چندسویه امن با قابلیت تکرار
In secure multiparty computation (SMC), a group of users jointly and securely computes a mathematical function on their private inputs, such that the privacy of their private inputs will be preserved. One of the widely used applications of SMC is the secure multiparty summation which securely computes the summation value of the users’ private inputs. In this paper, we consider a secure multipar...
متن کاملAlmost Every Set in Exponential Time is P-Bi-Immune
A set A is P-bi-immune if neither A nor its complement has an innnite subset in P. We investigate here the abundance of P-bi-immune languages in linear-exponential time (E). We prove that the class of P-bi-immune sets has measure 1 in E. This implies thatàlmost' every language in E is P-bi-immune, that is to say, almost every set recognizable in linear exponential time has no algorithm that rec...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Arch. Math. Log.
دوره 54 شماره
صفحات -
تاریخ انتشار 2015