The question of how complex a leaf language must be in order to characterize some given class C is investigated, which leads to the examination of the closure of different language classes under bit-reducibility.Expand

An upper bound for L #L in terms of computation of integer determinants is given from which it is concluded that all logspace counting classes are contained in NC2.Expand

An upper bound for in terms of computation of integer determinants is given from which it is concluded that all logspace counting classes are contained in.Expand

It is proved that constant depth circuits of size nlogO(1)n over the basis AND, OR, PARITY are no more powerful than circuits of this size with depth four and the size bound n logO( 1)n is optimal when considering depth reduction over AND, Or, and PARITY.Expand

An (m, n)-computation of a function f is given by a deterministic Turing machine which on n pairwise different inputs produces n output values where at least m of the n values are in accordance with f and the analogue of Trakhtenbrot's result holds.Expand

M-valued locally definable acceptance types are introduced, a new model generalizing the idea of alternating machines and their acceptance behaviour, by proving a normal form theorem stating that for every finite acceptancetype there exists a finite acceptance type that characterizes the same class, but consists only of one binary function.Expand