Hard Promise Problems and Nonuniform Complexity

Nondeterministically Selective Sets

In this note, we study NP-selective sets (formally, sets that are selective via NPSVt functions) as a natural generalization of P-selective sets. We show that, assuming P 6 = NP \coNP, the class of NP-selective sets properly contains the class of P-selective sets. We study several properties of NP-selective sets such as self-reducibility, hardness under various reductions, lowness, and nonunifo...

Nonuniform Hard Boolean Functions and Uniform Complexity Classes

Completeness and Weak Completeness Under Polynomial-Size Circuits

This paper investigates the distribution and nonuniform complexity of problems that are com plete or weakly complete for ESPACE under nonuniform reductions that are computed by polynomial size circuits P Poly Turing reductions and P Poly many one reductions A tight exponential lower bound on the space bounded Kolmogorov complexities of weakly P Poly Turing complete problems is established A Sma...

Parallelizing Assignment Problem with DNA Strands

Background:Many problems of combinatorial optimization, which are solvable only in exponential time, are known to be Non-Deterministic Polynomial hard (NP-hard). With the advent of parallel machines, new opportunities have been emerged to develop the effective solutions for NP-hard problems. However, solving these problems in polynomial time needs massive parallel machines and ...

On the Complexity of Restoring Corrupted Colorings

In the r-Fix problem, we are given a graph G, a (non-proper) vertex-coloring c : V (G) → [r], and a positive integer k. The goal is to decide whether a proper r-coloring c′ is obtainable from c by recoloring at most k vertices of G. Recently, Junosza-Szaniawski, Liedloff, and Rzążewski [SOFSEM 2015] asked whether the problem has a polynomial kernel parameterized by the number of recolorings k. ...