For completeness, sublogarithmic space is no space

It is shown that for any class C closed under linear-time reductions, the complete sets for C under sublogarithmic reductions are also complete under 2DFA reductions, and thus are isomorphic under first-order reductions

On the isomorphism conjecture for 2DFA reductions

The degree structure of complete sets under 2DFA reductions is investigated. It is shown that, for any class C that is closed under log-lin reductions: All complete sets for the class C under 2DFA reductions are also complete under one-one, length-increasing 2DFA reductions and are first-order isomorphic. The 2DFA-isomorphism conjecture is false, i.e., the complete sets under 2DFA reductions are not isomorphic to each other via 2DFA reductions

DSPACE(n)=<SUP>2</SUP> NSPACE(n): a degree theoretic characterization

It is shown that the following are equivalent. 1. DSPACE(n)=NSPACE(n). 2. There is a nontrivial &#8804; 1-NLm-degree that coincides with &#8804;1-Lm-degree. 3. For every class C closed under log-lin reductions, the &#8804;1-NLm-complete degree of C coincides with the &#8804;1-Lm-complete degree of C