Article ID Journal Published Year Pages File Type
430223 Journal of Computer and System Sciences 2014 15 Pages PDF
Abstract

•Introduction of polynomial-time tree reducibility (ptt-reducibility).•Correspondence between ptt-reducibility and inclusions between complexity classes.•The first levels of the dot-depth hierarchy are closed under ptt-reducibility.•Gap theorem of leaf-language definability above the Boolean closure of NP.

We introduce the polynomial-time tree reducibility (ptt-reducibility) for formal languages. Our main result establishes a one–one correspondence between this reducibility and inclusions between complexity classes. More precisely, for languages B and C it holds that B ptt-reduces to C if and only if the unbalanced leaf-language class of B is robustly contained in the unbalanced leaf-language class of C. Formerly, such correspondence was only known for balanced leaf-language classes. Moreover, we show that restricted to regular languages, the levels 0, 1/2, 1, and 3/2 of the dot-depth hierarchy are closed under ptt-reducibility. Our results also have applications in complexity theory: We obtain the first gap theorem of leaf-language definability above the Boolean closure of NP.

Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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