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Andreevs Problem states the following: Given an integer $d$ and a subset of $S subseteq mathbb{F}_q times mathbb{F}_q$, is there a polynomial $y = p(x)$ of degree at most $d$ such that for every $a in mathbb{F}_q$, $(a,p(a)) in S$? We show an $text{AC}^0[oplus]$ lower bound for this problem. This problem appears to be similar to the list recovery problem for degree $d$-Reed-Solomon codes over $mathbb{F}_q$ which states the following: Given subsets $A_1,ldots,A_q$ of $mathbb{F}_q$, output all (if any) the Reed-Solomon codewords contained in $A_1times cdots times A_q$. For our purpose, we study this problem when $A_1, ldots, A_q$ are random subsets of a given size, which may be of independent interest.
We extend the definitions of complexity measures of functions to domains such as the symmetric group. The complexity measures we consider include degree, approximate degree, decision tree complexity, sensitivity, block sensitivity, and a few others.
A matching is a set of edges in a graph with no common endpoint. A matching $M$ is called acyclic if the induced subgraph on the endpoints of the edges in $M$ is acyclic. Given a graph $G$ and an integer $k$, Acyclic Matching Problem seeks for an acy
The isomorphism problem is known to be efficiently solvable for interval graphs, while for the larger class of circular-arc graphs its complexity status stays open. We consider the intermediate class of intersection graphs for families of circular ar
We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q>1 and a graph G, the goal is to find a coloring of the edges of G with the maximu
Set disjointness is a central problem in communication complexity. Here Alice and Bob each receive a subset of an n-element universe, and they need to decide whether their inputs intersect or not. The communication complexity of this problem is relat