ContactPerson: aduri@cse.buffalo.edu ### Begin Citation ### Do not delete this line ### %R 2001-02 %U /u0/csgrad/aduri/tmp/file.ps %A Pavan, A. %A Selman, A.L. %T Separation of NP-completeness Notions %D January 16, 2001 %I Department of Computer Science and Engineering, SUNY Buffalo %X We use hypotheses of structural complexity theory to separate various NP-completeness notions. In particular, we introduce an hypothesis from which we describe a set in NP that is $\T$-complete but not $\tt$-complete. We provide fairly thorough analyses of the hypotheses that we introduce.