The universality of polynomial time Turing equivalence
نویسنده
چکیده
We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel sets of these equivalence relations which are related to Martin’s ultrafilter on the Turing degrees.
منابع مشابه
Some Afterthoughts on Hoppeld Networks
The present paper investigates four relatively independent issues, each in one section, which complete our knowledge regarding the computational aspects of popular Hoppeld nets 9]. In Section 2, the computational equivalence of convergent asymmetric and Hoppeld nets is shown with respect to the network size. In Section 3, the convergence time of Hoppeld nets is analyzed in terms of bit represen...
متن کاملSome Afterthoughts on Hopfield Networks
The present paper investigates four relatively independent issues each in one section which complete our knowledge regarding the computational aspects of popular Hop eld nets In Section the computational equivalence of convergent asymmetric and Hop eld nets is proved with respect to the network size In Section the convergence time of Hop eld nets is analyzed in terms of bit representations In S...
متن کاملUniformity, Universality, and Computability Theory
We prove a number of results motivated by global questions of uniformity in computability theory, and universality of countable Borel equivalence relations. Our main technical tool is a game for constructing functions on free products of countable groups. We begin by investigating the notion of uniform universality, first proposed by Montalbán, Reimann and Slaman. This notion is a strengthened ...
متن کاملUniformity, Universality, and Recursion Theory
We prove a number of results motivated by global questions of uniformity in recursion theory, and some longstanding open questions about universality of countable Borel equivalence relations. Our main technical tool is a class of games for constructing functions on free products of countable groups. These games show the existence of refinements of Martin’s ultrafilter on Turing invariant sets t...
متن کاملSome Considerations on Universality
Without the investigation of the concept of universality it is quite possible that our modern computers wouldn’t exist. Although they are finite automata, at least theoretically, practically they can be treated as Turing machines processing any special program which can be seen as a special Turing machine. This paper presents some general considerations on that concept, presenting in some more ...
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:
- Mathematical Structures in Computer Science
دوره 28 شماره
صفحات -
تاریخ انتشار 2018