Skip to main content


eCommons@Cornell

eCommons@Cornell >
College of Engineering >
Computer Science >
Computer Science Technical Reports >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/6239
Title: On Effective Speed-up and Long Proofs of Trivial Theorems in Formal Theories
Authors: Hartmanis, Juris
Keywords: computer science
technical report
Issue Date: Jul-1975
Publisher: Cornell University
Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR75-254
Abstract: In this note we give a very simple proof which shows that in many interesting formal mathematical theories, axiomatizable as well as decidable ones, for every given formalization we can effectively find infinite subsets of trivially true theorems which require as long proofs in the given formalism as the hardest theorems of the theory. Thus showing that for these theories every formalism is doomed to be blind to the triviality of infinite sets of theorems, which can be found effectively. Furthermore, it follows that for all (sufficiently large) constructable tape and time bounds there exists sets whose recognition can be effectively speeded up on infinite subsets and that such sets appear naturally, thus showing that for many concrete problems, every algorithm can be effectively sped-up on infinite subsets.
URI: http://hdl.handle.net/1813/6239
Appears in Collections:Computer Science Technical Reports
Hartmanis, Juris

Files in This Item:

File Description SizeFormat
75-254.pdf819.57 kBAdobe PDFView/Open
75-254.ps448.32 kBPostscriptView/Open

Refworks Export

Items in eCommons are protected by copyright, with all rights reserved, unless otherwise indicated.

 

© 2014 Cornell University Library Contact Us