On the Applicability of Post's Lattice
Computational Complexity
2012-01-06 v3 Logic in Computer Science
Abstract
For decision problems P defined over Boolean circuits from a restricted set of gates, we have that P(B) AC0 many-one reduces to P(B') for all finite sets B and B' of gates such that all gates from B can be computed by circuits over gates from B'. In this paper, we show that a weaker version of this statement holds for decision problems defined over Boolean formulae, namely that P(B) NC2 many-one reduces to P(B' union {and,or}) and that P(B) NC2 many-one reduces to P(B' union {false,true}), for all finite sets B and B' of Boolean functions such that all f in B can be defined in B'.
Cite
@article{arxiv.1007.2924,
title = {On the Applicability of Post's Lattice},
author = {Michael Thomas},
journal= {arXiv preprint arXiv:1007.2924},
year = {2012}
}