… information in the object, the depth thus represents the amount of “computational … (Depth
is closely related to Adleman’s notion of “potential” … One way to investigate the computational …

… Abstract. This paper investigates Bennett's notions of strong and weak computational depth
(also called logical depth) for … All proofs and lemmas are omitted from this extended abstract. …

… The definition of application is that of evaluating an e-reduction: If x, yare variables in the …
A-abstraction describes how we define an e-operator from an re set Ax.r = {(m,D) 1m E r[D/x]} …

… In our preconditioning step we compute C and 7) using Theorem 14 with our cover algorithm.
We also compute the d-topset, where d is the depth of the deepest subterm s ET(C, X) of a …

Abstract This paper introduces two complexity-theoretic formulations of Bennett’s logical
depth: finite-state depth and polynomial-time depth. It is shown that for both formulations, trivial …

… Abstract We discuss a number of results regarding an im- portant subject: the study of the
computational power of depth… 2.2 Nonadaptive logspace reducibility Given a class of functions F…

… In our case, we need a reduction in the base case of the argument to a lower bound for
index-width, … Let us note that the reduction described above is to a formula that has large depth. In …

… time, and that there are two states of maximal depth, exactly one of which is … a circuit of size
s and depth d over n variables … might be more appropriately modeled with abstract operators …

… -- then the computational depth of x is the amount of time required for a computation to derive
x from … If F is a uniform reducibility that is (like all standard reducibitities) reflexive, then the …

… In this extended abstract we give a representation theorem for … by polynomial-size logarithmic
depth arithmetic circuits. #… I will talk about this reduction and some related techniques. I …