Continuing a line of investigation that has studied the function classes #P, #SAC^1, #L, and #NC^1, we study the class of functions #AC^0. One way to define #AC^0 is as the class of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication gates. In contrast to ... 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 extraction to these complexity classes. ... more >>>

We show that the counting classes AWPP and APP [Li 1993] are more robust than previously thought. Our results identify asufficient condition for a language to be low for PP, and we show that this condition is at least as weak as other previously studied criteria. Our results imply that ... more >>>

Following the approach of Hemaspaandra and Vollmer, we can define counting complexity classes #.C for any complexity class C of decision problems. In particular, the classes #.Pi_{k}P with k >= 1 corresponding to all levels of the polynomial hierarchy have thus been studied. However, for a large variety of counting ... more >>>