Computable real function F such that F is not polynomial time computable on [0, 1]
نویسنده
چکیده
A computable real function F on [0,1] is constructed such that there exists an exponential time algorithm for the evaluation of the function on [0,1] on Turing machine but there does not exist any polynomial time algorithm for the evaluation of the function on [0,1] on Turing machine (moreover, it holds for any rational point on (0,1))
منابع مشابه
Functions That Preserve p-Randomness
We show that polynomial-time randomness (p-randomness) is preserved under a variety of familiar operations, including addition and multiplication by a nonzero polynomial-time computable real number. These results follow from a general theorem: If I ⊆ R is an open interval, f : I → R is a function, and r ∈ I is p-random, then f(r) is p-random provided 1. f is p-computable on the dyadic rational ...
متن کاملInvitation to Real Complexity Theory: Algorithmic Foundations to Reliable Numerics with Bit-Costs
While concepts and tools from Theoretical Computer Science are regularly applied to, and significantly support, software development for discrete problems, Numerical Engineering largely employs recipes and methods whose correctness and efficiency is demonstrated empirically. We advertise Real Complexity Theory : a resource-oriented foundation to rigorous computations over continuous universes s...
متن کاملNotes on space complexity of integration of computable real functions in Ko-Friedman model
In the present paper it is shown that real function g(x) = x 0 f (t)dt is a linear-space computable real function on interval [0, 1] if f is a linear-space computable C 2 [0, 1] real function on interval [0, 1], and this result does not depend on any open question in the computational complexity theory. The time complexity of computable real functions and integration of computable real function...
متن کامل#p-complete Conditional Distributions
We study conditional probability from the perspective of complexity theory of functions and operators in analysis, building on work by Ko (1983), Friedman (1984), and Kawamura and Cook (2010). For some random variable X in {0, 1}N whose distribution is continuous and polynomial-time computable, and some polynomial-time computable function f : {0, 1}N → [0, 1] for which the random variable f(X) ...
متن کاملRelative computability and uniform continuity of relations
A type-2 computable real function is necessarily continuous; and this remains true for computations relative to any oracle. Conversely, by the Weierstrass Approximation Theorem, every continuous f : [0; 1]→ R is computable relative to some oracle. In their search for a similar topological characterization of relatively computable multi-valued functions f : [0; 1] ⇒ R (also known as multi-functi...
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:
- CoRR
دوره abs/1404.7053 شماره
صفحات -
تاریخ انتشار 2014