We describe a new deterministic algorithm for the problem of constructing k-th power nonresidues in nite elds GF(p n), where p is prime and k is a prime divisor of p n ?1. We prove under the assumption of the Extended Riemann Hypothesis (ERH), that for xed n and p ! 1, our algorithm runs in polynomial time. Unlike previous algorithms for this problem, this polynomial time bound holds even if k ...

LetM=(E, I) be a matroid, and let S be a family of subsets of size p of E. A subfamily Ŝ ⊆ S represents S if for every pair of sets X ∈S and Y ⊆E\X such that X∪Y ∈ I, there is a set X̂ ∈ Ŝ disjoint from Y such that X̂∪Y ∈I. In this paper, we present a fast computation of representative families for uniform matroids. We use our computation to develop deterministic algorithms that solve k-Partial C...

In this article, we study algorithms for dynamic networks with asynchronous start, i.e., each node may start running the algorithm in a different round. Inactive nodes transmit only heartbeats, which contain no information but can be detected by active nodes. We make no assumption on the way the nodes are awakened, except that for each node u there is a time su in which it is awakened and start...

In this paper the behavior of conditional communication in the presence of priority will be described. In the theory of CSP, conditional communications are expressed by a (external) choice construct—also known as the alternative construct—by which the choice of one communication out of a set of communications is non-deterministic. In practice, some communication can be more important than other...

We consider the design of an optimal mechanism for a seller selling two items to a single buyer so that the expected revenue to the seller is maximized. The buyer’s valuation of the two items is assumed to be the uniform distribution over an arbitrary rectangle [c1, c1 + b1] × [c2, c2 + b2] in the positive quadrant. The solution to the case when (c1, c2) = (0, 0) was already known. We provide a...

We investigate weak recognizability of deterministic languages of infinite trees. We prove that for deterministic languages the Borel hierarchy and the weak index hierarchy coincide. Furthermore, we propose a procedure computing for a deterministic automaton an equivalent minimal index weak automaton with a quadratic number of states. The algorithm works within the time of solving the emptiness...

We analyze the routing of k-permutations on circular processor arrays connected by bidirectional links. In contrast to linear processor arrays, it is hard to prove lower bounds for the routing time or to construct eecient algorithms for routing k-permutations on circular arrays (except for the case k = 1). We will prove non-trivial lower bounds for routing with global knowledge and for routing ...

In this paper we present a deterministic algorithm to compute the number of F^-points of an elliptic curve that is defined over a finite field Fv and which is given by a Weierstrass equation. The algorithm takes 0(log9 q) elementary operations. As an application wc give an algorithm to compute square roots mod p. For fixed .ï e Z, it takes 0(log9p) elementary operations to compute fx mod p.

Consider an N×n random matrix Yn = (Y n ij ) where the entries are given by Y ij = σij (n) √ n X ij , the X n ij being independent and identically distributed, centered with unit variance and satisfying some mild moment assumption. Consider now a deterministic N × n matrix An whose columns and rows are uniformly bounded in the Euclidean norm. Let n = Yn +An. We prove in this article that there ...

It is well known that every finite Abelian group G can be represented as a product of cyclic groups: G = G1×G2×· · ·Gt, where each Gi is a cyclic group of size p j for some prime p and integer j ≥ 1. If ai is the generator of the cyclic group of Gi, i = 1, 2, · · · , t, then the elements a1, a2, · · · , at are the basis of G. In this paper, we first obtain an O(n)-time deterministic algorithm f...