We have recently shown that q-gram filters based on gapped q-grams instead of the usual contiguous q-grams can provide orders of magnitude faster and/or more efficient filtering for the Hamming distance. In this paper, we extend the results for the Levenshtein distance, which is more problematic for gapped q-grams because an insertion or deletion in a gap affects a q-gram while a replacement do...

Resolution proof systems for quantified Boolean formulas (QBFs) provide a formal model for studying the limitations of state-of-the-art search-based QBF solvers that use these systems to generate proofs. We study a proof system that combines two proof systems supported by the solver DepQBF: Q-resolution with generalized universal reduction according to a dependency scheme and long distance Q-re...

In this paper we deal with a problem of Turán concerning the ‘distance’ of polynomials to irreducible polynomials. Using computational methods we prove that for any monic polynomial P ∈ Z[x] of degree ≤ 22 there exists a monic polynomial Q ∈ Z[x] with deg(Q) = deg(P ) such that Q is irreducible over Q and the ‘distance’ of P and Q is ≤ 4.

Motivated by the application of high-density data storage technologies, symbol-pair codes are proposed to protect against pair-errors in symbol-pair channels, whose outputs are overlapping pairs of symbols. The research of symbol-pair codes with large minimum pair-distance is interesting since such codes have the best possible error-correcting capability. A symbol-pair code attaining maximal mi...

In this Appendix, we summarize some basic properties of the three classes of functional diversity measures: (1) functional Hill number ) (Q D q which quantifies the effective number of equally abundant and equally distinct species in an assemblage with a constant species pairwise distance Q, where Q denotes Rao’s quadratic entropy; (2) mean functional diversity MD(Q) = Q Q D q × )] ( [ which qu...

Let be a distance-regular graph of diameter d, valency k and r := max{i | (ci , bi ) = (c1, b1)}. Let q be an integer with r + 1 ≤ q ≤ d − 1. In this paper we prove the following results: Theorem 1 Suppose for any pair of vertices at distance q there exists a strongly closed subgraph of diameter q containing them. Then for any integer i with 1 ≤ i ≤ q and for any pair of vertices at distance i ...

In this paper, we present the exact Hausdorff distance between the offset curve of quadratic Bézier curve and its quadratic GC1 approximation. To illustrate the formula for the Hausdorff distance, we give an example of the quadratic GC1 approximation of the offset curve of a quadratic Bézier curve. 1. Preliminaries Quadratic Bézier curves and their offset curves are widely used in CAD/CAM or Co...