## P-selective Self-reducible sets: A New Characterization of P (1996)

Venue: | In Proceedings of the 8th Structure in Complexity Theory Conference |

Citations: | 27 - 6 self |

### BibTeX

@INPROCEEDINGS{Buhrman96p-selectiveself-reducible,

author = {Harry Buhrman and Leen Torenvliet},

title = {P-selective Self-reducible sets: A New Characterization of P},

booktitle = {In Proceedings of the 8th Structure in Complexity Theory Conference},

year = {1996},

pages = {44--51},

publisher = {IEEE Computer Society Press}

}

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### Abstract

We show that any p-selective and self-reducible set is in P . As the converse is also true, we obtain a new characterization of the class P . A generalization and several consequences of this theorem are discussed. Among other consequences, we show that under reasonable assumptions auto-reducibility and self-reducibility differ on NP , and that there are non-p-T -mitotic sets in NP . 1 Introduction Separating complexity classes is a very popular, but rarely won game in complexity theory. Frustrated by misfortune, computer scientists have often turned to attempts of characterizing complexity classes in a different way. The hopes are, that the new characterization of the complexity class may provide new insights and a `handle' to force the separation where earlier attempts have failed. Well-known examples of this are the many ways to define the class of sets for which there exist small circuits [Pip79], and the identification of various forms of interactive proof systems with stan...