Document Type


Publication Date



Glaßer et al. (SIAMJCOMP 2008 and TCS 2009)2 proved existence of two sparse sets A and B in EXP, where A is 3-tt (truth-table) polynomial-time autoreducible but not weakly polynomial-time Turing mitotic and B is polynomial-time 2-tt autoreducible but not weakly polynomial-time 2-tt mitotic. We unify and strengthen both of those results by showing that there is a sparse set in EXP that is polynomial-time 2-tt autoreducible but not even weakly polynomial-time Turing mitotic. All these results indicate that polynomial-time autoreducibilities in general do not imply polynomial-time mitoticity at all with the only exceptions of the many-one and 1-tt reductions. On the other hand, however, we proved that every autoreducible set for the polynomial-time bounded disjunctive or conjunctive tt reductions is weakly mitotic for the polynomial-time tt reduction that makes logarithmically many queries only. This shows that autoreducible sets for reductions making more than one query could still be mitotic in some way if they possess certain special properties.


Original published version available at

Publication Title

Theoretical Computer Science





To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.