Abstract not found

Many of the \n 2-hard " problems described by Gajentaan and Overmars can be solved using limited nondeterminism or other sharply-bounded quanti ers. Thus we suggest that these problems are not among the hardest problems solvable in quadratic time.

We de ne the notion of adding \small amounts " of nondeterminism to a deterministic function class, and give a machine model � the result is a functional AC 0 closure of the deterministic class. We characterize, by the \safe parameters " technique, the classes of functions computable in linear and in quasilinear time on a multi-tape Turing machine. We thencombine these two results by extending the \safe parameters " characterizations to the functions computable in (quasi)linear time with small amounts of nondeterminism, and discuss implications for both sequential and parallel complexity.

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...

Many of the "n²-hard" problems described by Gajentaan and Overmars can be solved using limited nondeterminism or other sharply-bounded quanti ers. Thus we suggest that these problems are not among the hardest problems solvable in quadratic time.