We investigate the phenomenon of depth-reduction in commutative
and non-commutative arithmetic circuits. We prove that in the
commutative setting, uniform semi-unbounded arithmetic circuits of
logarithmic depth are as powerful as uniform arithmetic circuits of
polynomial degree; earlier proofs did not work in the ... more >>>

The aim of this paper is to use formal power series techniques to
study the structure of small arithmetic complexity classes such as
GapNC^1 and GapL. More precisely, we apply the Kleene closure of
languages and the formal power series operations of inversion and
root ... more >>>