Combinatorial testing makes it possible to test large systems effectively while maintaining certain coverage guarantees. At the same time, construction of optimized covering arrays (CAs) with a number columns is challenging task. Heuristic and Metaheuristic approaches often become inefficient when applied instances, as computation quality for new moves or solutions during search becomes too slo...

Aslam presents an algorithm he claims will count the number of perfect matchings in any incomplete bipartite graph with an algorithm in the function-computing version of NC, which is itself a subset of FP. Counting perfect matchings is known to be #P-complete; therefore if Aslam's algorithm is correct, then NP=P. However, we show that Aslam's algorithm does not correctly count the number of per...

A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this en...

In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if B ⊆ 2 is a Gδσ-set then either B is countable or B contains a perfect subset. Second, we prove that if 2 is the countable union of countable sets, then there exists an Fσδ set C ⊆ 2 such that C is uncountable but contains no perfect subset. Finally, we c...

Let G be a bipartite graph with bicoloration {A, B}, |A| = |B|, and let w : E(G) -» K where K is a finite abelian group with k elements. For a subset S c E(G) let w(S) = IIeE s (e).A Perfect matching M c E(G) is a w-matching if w(M) = 1. A characterization is given for all w's for which every perfect matching is a w-matching. It is shown that if G = Kk+1,k+1 then either G has no w-matchings or ...

This paper introduces a general class of -channel linear phase perfect reconstruction filter banks (FBs) with rational coefficients. A subset of the presented solutions has dyadic coefficients, leading to multiplierless implementations suitable for lowpower mobile computing. All of these FBs are constructed from a lattice structure that is VLSI-friendly, employs the minimum number of delay elem...

A set X ⊆ 2 has property (s) (Marczewski (Szpilrajn)) iff for every perfect set P ⊆ 2 there exists a perfect set Q ⊆ P such that Q ⊆ X or Q∩X = ∅. Suppose U is a nonprincipal ultrafilter on ω. It is not difficult to see that if U is preserved by Sacks forcing, i.e., it generates an ultrafilter in the generic extension after forcing with the partial order of perfect sets, then U has property (s)...

Minimal perfect hash functions have been shown to be useful to compress data in several data management tasks. In particular, order-preservingminimal perfect hash functions [12] have been used to retrieve the position of a key in a given list of keys: however, the ability to preserve any given order leads to an unavoidable (n log n) lower bound on the number of bits required to store the funct...

V := {ri}i=1 ∪ {ci}i=1 and E := {{ri, cj} | mi,j ≥ 1/n}. The main observation is that if G contains a perfect matching then there exists a desired permutation. To see that, let us assume that P = {e1, . . . , en} is a subset of the edges of G which form a perfect matching, with ei = {ri, cji}. Then setting π(i) := ji satisfies the desired properties: since P is a matching we have that π is a bi...