On Unification Modulo One-Sided Distributivity: Algorithms, Variants and Asymmetry

An algorithm for unification modulo one-sided distributivity is an early result by Tid\'en and Arnborg. More recently this theory has been of interest in cryptographic protocol analysis due to the fact that many cryptographic operators satisfy this property. Unfortunately the algorithm presented in the paper, although correct, has recently been shown not to be polynomial time bounded as claimed. In addition, for some instances, there exist most general unifiers that are exponentially large with respect to the input size. In this paper we first present a new polynomial time algorithm that solves the decision problem for a non-trivial subcase, based on a typed theory, of unification modulo one-sided distributivity. Next we present a new polynomial algorithm that solves the decision problem for unification modulo one-sided distributivity. A construction, employing string compression, is used to achieve the polynomial bound. Lastly, we examine the one-sided distributivity problem in the new asymmetric unification paradigm. We give the first asymmetric unification algorithm for one-sided distributivity

The role of natural resources in the livelihoods of the urban poor

This publication is based on briefing material commissioned for the European Union (EU). The EU briefing papers have sub-Saharan Africa as their primary focus, though case study material may also be drawn from Caribbean and Pacific country experience. The information they contain is based principally on a review of secondary data and documentation, although some specific aspects have been explored through short, focused field studies. The publication is divided into three sections: this introductory section provides an overview of urbanization in developing regions, and introduces key issues of migration, employment, the areas of interface with the agriculture and the rural economy, and the nature of urban poverty; the second section focuses on the details of how poor people in urban areas use natural resources, and how natural resources affect their livelihoods and well-being; and the last section builds on the analysis of the nature of urban poverty, and its interaction with natural resources, to propose appropriate pro-poor policies and direct intervention, taking into account the importance of natural resources to the urban poor

Unification modulo a partial theory of exponentiation

Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.Comment: In Proceedings UNIF 2010, arXiv:1012.455

Finding the Needles in the Haystacks: High-Fidelity Models of the Modern and Archean Solar System for Simulating Exoplanet Observations

We present two state-of-the-art models of the solar system, one corresponding to the present day and one to the Archean Eon 3.5 billion years ago. Each model contains spatial and spectral information for the star, the planets, and the interplanetary dust, extending to 50 AU from the sun and covering the wavelength range 0.3 to 2.5 micron. In addition, we created a spectral image cube representative of the astronomical backgrounds that will be seen behind deep observations of extrasolar planetary systems, including galaxies and Milky Way stars. These models are intended as inputs to high-fidelity simulations of direct observations of exoplanetary systems using telescopes equipped with high-contrast capability. They will help improve the realism of observation and instrument parameters that are required inputs to statistical observatory yield calculations, as well as guide development of post-processing algorithms for telescopes capable of directly imaging Earth-like planets.Comment: Accepted for publication in PAS