Summary: DSPACE(n) ?
= NSPACE(n): A Degree Theoretic
Department of Computer Science and Engineering
Indian Institute of Technology, Kanpur 208016, INDIA
It is shown that the following are equivalent.
1. DSPACE(n) = NSPACE(n).
2. There is a non-trivial 1-NL
m -degree that coincides with a 1-L
3. For every class C closed under log-lin reductions, the 1-NL
m -complete degree of C
coincides with the 1-L
m -complete degree of C.
The structure of complete degrees has been extensively investigated over the years. Particular at-
tention has been paid to the polynomial-time many-one complete degrees (in short, p