Computational depth and reducibility
نویسندگان
چکیده
منابع مشابه
Computational Depth and Reducibility
This paper reviews and investigates Bennett s notions of strong and weak computational depth also called logical depth for in nite binary sequences Roughly an in nite binary sequence x is de ned to be weakly useful if every element of a non negligible set of decidable sequences is reducible to x in recursively bounded time It is shown that every weakly useful sequence is strongly deep This resu...
متن کاملA Reducibility for the Dot-Depth Hierarchy
Hierarchies considered in computability theory and in complexity theory are related to some reducibilities in the sense that levels of the hierarchies are downward closed and have complete sets. In this paper we propose a reducibility having similar relationship to the Brzozowski’s dot-depth hierarchy and some its refinements. We prove some basic facts on the corresponding degree structure and ...
متن کاملComputational Depth
We introduce Computational Depth, a measure for the amount of “nonrandom” or “useful” information in a string by considering the difference of various Kolmogorov complexity measures. We investigate three instantiations of Computational Depth: Basic Computational Depth, a clean notion capturing the spirit of Bennett’s Logical Depth. Time-t Computational Depth and the resulting concept of Shallow...
متن کاملComputational depth: Concept and applications
We introduce Computational Depth, a measure for the amount of “nonrandom” or “useful” information in a string by considering the difference of various Kolmogorov complexity measures. We investigate three instantiations of Computational Depth: – Basic Computational Depth, a clean notion capturing the spirit of Bennett’s Logical Depth. We show that a Turing machine M runs in time polynomial on av...
متن کاملRecursive Computational Depth
In the s Bennett introduced computational depth as a formal measure of the amount of computational history that is evident in an object s structure In particular Bennett identi ed the classes of weakly deep and strongly deep sequences and showed that the halting problem is strongly deep Juedes Lath rop and Lutz subsequently extended this result by de ning the class of weakly useful sequences an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1994
ISSN: 0304-3975
DOI: 10.1016/0304-3975(94)00014-x