Inferring Termination Conditions for Logic Programs using Backwards Analysis

This paper focuses on the inference of modes for which a logic program is guaranteed to terminate. This generalises traditional termination analysis where an analyser tries to verify termination for a specified mode. Our contribution is a methodology in which components of traditional termination analysis are combined with backwards analysis to obtain an analyser for termination inference. We identify a condition on the components of the analyser which guarantees that termination inference will infer all modes which can be checked to terminate. The application of this methodology to enhance a traditional termination analyser to perform also termination inference is demonstrated

Low-Degree Spanning Trees of Small Weight

The degree-d spanning tree problem asks for a minimum-weight spanning tree in which the degree of each vertex is at most d. When d=2 the problem is TSP, and in this case, the well-known Christofides algorithm provides a 1.5-approximation algorithm (assuming the edge weights satisfy the triangle inequality). In 1984, Christos Papadimitriou and Umesh Vazirani posed the challenge of finding an algorithm with performance guarantee less than 2 for Euclidean graphs (points in R^n) and d > 2. This paper gives the first answer to that challenge, presenting an algorithm to compute a degree-3 spanning tree of cost at most 5/3 times the MST. For points in the plane, the ratio improves to 3/2 and the algorithm can also find a degree-4 spanning tree of cost at most 5/4 times the MST.Comment: conference version in Symposium on Theory of Computing (1994

A conjecture of Erdős, supersingular primes and short character sums

If k is a sufficiently large positive integer, we show that the Diophantine equation n(n+d)⋯(n+(k−1)d)=yℓ has at most finitely many solutions in positive integers n,d,y and ℓ, with gcd(n,d)=1 and ℓ≥2. Our proof relies upon Frey-Hellegouarch curves and results on supersingular primes for elliptic curves without complex multiplication, derived from upper bounds for short character sums and sieves, analytic and combinatorial

Pandemic (H1N1) 2009 Cluster Analysis: A Preliminary Assessment

Pandemic (H1N1) 2009 virus has been causing major concerns around the world because of its epidemic potential, rapid dissemination, rate of mutations, and the number of fatalities. One way to gain an advantage over this virus is to use existing rapid bioinformatics tools to examine easily and inexpensively generated genetic sequencing data. We have used the protein sequences deposited with the National Center for Biotechnology Information (NCBI) for data mining to study the relationship among the Pandemic (H1N1) 2009 proteins. There are 11 proteins in the Pandemic (H1N1) 2009 virus, and analysis of sequences from 65 different locations around the globe has resulted in two major clusters. These clusters illustrate the Pandemic H1N1 2009 virus is already experiencing significant genetic drift and that rapid worldwide travel is affecting the distribution of genetically distinct isolates