The Euclid Abstract Machine

نویسندگان

  • Jerzy Mycka
  • José Félix Costa
  • Francisco Coelho
چکیده

Concrete non-computable functions are usually related to the halting function. Is it possible to present examples of non-computability, which are unrelated to the halting problem and its derivatives? We built an abstract machine based on the historic concept of compass and ruler constructions (a compass construction would suffice) which reveals the existence of non-computable functions not related with the halting problem. These natural, and the same time, non-computable functions can help to understand the nature of the uncomputable and the purpose, the goal, and the meaning of computing beyond Turing.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The Euclid Abstract Machine: Trisection of the Angle and the Halting Problem

What is the meaning of hypercomputation, the meaning of computing more than the Turing machine? Concrete non-computable functions always hide the halting problem as far as we know. Even the construction of a function that grows faster than any recursive function — the Busy Beaver — a more natural function, hides the halting function, that can easily be put in relation with the Busy Beaver. Is t...

متن کامل

Historical Developments in Computers to the 1950 s 1

The start of the computer revolution is considered to have taken place with the development of the ENIAC electronic digital computer in 1946, slightly more than 50 years ago, at the Moore School of Electrical Engineering at the University of Pennsylvania. I will trace the the scientiic developments that led to the ENIAC and other computers developed at around the same time. In antiquity, Euclid...

متن کامل

NOTES ON TIlE DESIGN OF EUCLID

Euclid is a language for writing system programs that are to be verified. We believe that verification and reliability are closely related, because if it is hard to reason about programs using a language feature, it will be diff icult to write programs that use it properly. This pape, discusses a number of issues in the design of Euclid, including such topics as the scope of names, aliasing, mo...

متن کامل

Thinkit’s Submissions for Mirex2009 Audio Music Classification and Similarity Tasks

This full abstract describes our submitted systems for the MIREX09 audio classification tasks (genre, mood, classical composer, audio tagging) and music similarity and retrieval task. All the classification systems are based on basic acoustic features (e.g. MFCC) and the modeling framework of GSV-SVM, which has been successfully applied in speaker recognition field. And the similarity systems a...

متن کامل

Smoothly Generic Graphs of Orthogonal Hulls and the Invertibility of Right-Pointwise Hyperbolic, Hyper-Prime Functionals

Let Zη be a Lobachevsky topos. Is it possible to construct isomorphisms? We show that there exists an Euclid–Cantor and canonical convex, onto subalgebra. We wish to extend the results of [14, 14] to almost surely de Moivre ideals. Recent developments in abstract probability [14] have raised the question of whether a ⊃ t̂(Ṽ ).

متن کامل

ذخیره 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 نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • IJUC

دوره 4  شماره 

صفحات  -

تاریخ انتشار 2008