A Precise Version of a Time Hierarchy Theorem

Authors:
Amir M. Ben-Amram;Neil D. Jones
Affiliations:
The Academic College of Tel-Aviv Yaffo, Tel-Aviv, Israel. amirben@server.mta.ac.il;(Correspd.) Department of Computer Science (DIKU), The University of Copenhagen, Denmark. neil@diku.dk
Venue:
Fundamenta Informaticae
Year:
1999

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Computational complexity via programming languages: constant factors do matter

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Abstract

Using a simple programming language as a computational model, Neil Jones has shown that a constant-factor time hierarchy exists: thus a constant-factor difference in time makes a difference in problem-solving power, unlike the situation with Turing machines. In this note we review this result and fill in the programming details in the proof, thus obtaining a precise version of the theorem with explicit constant factors. Specifically, multiplying the running time by 232 provably allows more decision problems to be solved.