Collapsing Exact Arithmetic Hierarchies [chapter]

Nikhil Balaji, Samir Datta
2014 Lecture Notes in Computer Science  
We provide a uniform framework for proving the collapse of the hierarchy, NC 1 (C) for an exact arithmetic class C of polynomial degree. These hierarchies collapses all the way down to the third level of the AC 0hierarchy, AC 0 3 (C). Our main collapsing exhibits are the classes C ∈ {C=NC 1 , C=L, C=SAC 1 , C=P}. NC 1 (C=L) and NC 1 (C=P) are already known to collapse [1, 18, 19] . We reiterate that our contribution is a framework that works for all these hierarchies. Our proof generalizes a
more » ... of from [8] where it is used to prove the collapse of the AC 0 (C=NC 1 ) hierarchy. It is essentially based on a polynomial degree characterization of each of the base classes.
doi:10.1007/978-3-319-04657-0_26 fatcat:m4umv2v5kjda5jjszwjzq67dni