We study the robustness of complete languages in PSPACE and prove that they are robust against P-selective sparse sets. Earlier similar results are known for EXP-complete sets [3] and NP-complete sets [7].

The many types of resource bounded reductions that are both object of study and research tool in structural complexity theory have given rise to a large variety of completeness notions. A complete set in a complexity class is a manageable object that represents the structure of the entire class

We study several properties of sets that are complete for NP. We prove that if L is an NP-complete set and S � ⊇ L is a p-selective sparse set, then L − S is ≤p m-hard for NP. We demonstrate existence of a sparse set S ∈ DTIME(22n) such that for every L ∈ NP − P, L − S is not ≤p m-hard for NP

We show that a set is m-autoreducible if and only if it is m-mitotic. This solves a long standing open question in a surprising way. As a consequence of this unconditional result and recent work by Gla6Ÿer et al., complete sets for all of the following complexity classes are m-mitotic: NP, coNP, â

. We show that there is a set which is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2 lin . Here a set A in a complexity class C is almost complete for C under some reducibility r if the class

This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and arises in many important applications as in the task

We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M. Can we complete the matrix and recover the entries that we have not seen? We show that one can

... We disprove the equivalence between autoreducibility and mitoticity for all polynomialtime-bounded reducibilities between 3-tt-reducibility and Turing-reducibility: There exists a sparse set in EXP that is polynomial-time 3-tt-autoreducible, but not weakly polynomial-time T

Abstract not found

, better documentation, easier installation, improved portability, and higher performance. This report contains a complete description of the tool set, including retrieval and installation instructions, a description of how to use the tools, a description of the target SimpleScalar architecture, and many