Hemachandra, Lane A.2007-04-232007-04-231987-07http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR87-852https://hdl.handle.net/1813/6692The class of near-testable sets, NT, was defined by Goldsmith, Joseph, and Young. They noted that $P \subseteq NT \subseteq PSPACE$, and asked whether P=NT. This note shows that NT shares the same $m$-degree as the parity-based complexity class $\bigoplus P$ (i.e., $NT\equiv^{p}_{m} \oplus P$) and uses this to prove that relative to a random oracle $A, P^{A} \neq NT^{A}$ with probability one. Indeed, with probability one, $NT^{A} - (NP^{A} \bigcup coNP^{A}) \neq 0$.738466 bytes199689 bytesapplication/pdfapplication/postscripten-UScomputer sciencetechnical reporttechnical report