Algebraic and Logical Characterizations of Deterministic Linear Time Classes (1996)
| Venue: | In Proc. 14th Symposium on Theoretical Aspects of Computer Science STACS 97 |
| Citations: | 1 - 1 self |
BibTeX
@INPROCEEDINGS{Schwentick96algebraicand,
author = {Thomas Schwentick},
title = {Algebraic and Logical Characterizations of Deterministic Linear Time Classes},
booktitle = {In Proc. 14th Symposium on Theoretical Aspects of Computer Science STACS 97},
year = {1996},
pages = {463--474}
}
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Abstract
In this paper an algebraic characterization of the class DLIN of functions that can be computed in linear time by a deterministic RAM using only numbers of linear size is given. This class was introduced by Grandjean, who showed that it is robust and contains most computational problems that are usually considered to be solvable in deterministic linear time. The characterization is in terms of a recursion scheme for unary functions. A variation of this recursion scheme characterizes DLINEAR, the class which allows polynomially large numbers. A second variation defines a class that still contains DTIME(n), the class of functions that are computable in linear time on a Turing machine. From these algebraic characterizations, logical characterizations of DLIN and DLINEAR as well as complete problems (under DTIME(n) reductions) are derived. 1 Introduction Although deterministic linear time is a frequently used notion in the theory of algorithms it still does not have a universally accept...
