Lower bounds and complete problems in nondeterministic linear time and sublinear space complexity classes

Philippe Chapdelaine; Etienne Grandjean

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arXiv · cs/0606058

Lower bounds and complete problems in nondeterministic linear time and sublinear space complexity classes

Philippe Chapdelaine·Etienne Grandjean

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Abstract

Proving lower bounds remains the most difficult of tasks in computational complexity theory. In this paper, we show that whereas most natural NP-complete problems belong to NLIN (linear time on nondeterministic RAMs), some of them, typically the planar versions of many NP-complete problems are recognized by nondeterministic RAMs in linear time and sublinear space. The main results of this paper are the following: as the second author did for NLIN, we give exact logical characterizations of nondeterministic polynomial time-space complexity classes; we derive from them a class of problems, which are complete in these classes, and as a consequence of such a precise result and of some recent separation theorems using diagonalization, prove time-space lower bounds for these problems.

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BibTeX RIS

Philippe Chapdelaine, Etienne Grandjean. 2006-06-13. Lower bounds and complete problems in nondeterministic linear time and sublinear space complexity classes. https://arxiv.org/abs/cs/0606058

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