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Abstract. The algorithm for mutual exclusion proposed by B. Szymanski is an interesting challenge for verification methods and tools. Several full proofs have been described in the literature, but they seem to require lengthy interactive sessions with powerful theorem provers. As far as this algorithm makes use of only the most elementary facts of arithmetics, we conjectured that a simple, non-interactive proof should exist; this paper gives such a proof, describes its development and how an elementaxy tool has been used to complete the verification.

Reproductive success of mallards (Anas platyrhynchos) is influenced by distribution and amount of wetlands and grasslands on the landscape during the breeding season. Most studies of mallard reproductive success have been conducted in areas with high wetland densities and large tracts of grasslands. We investigated nest survival of mallards in intensively cropped northern Iowa, USA, where wetland and grassland habitats were highly fragmented. We radiotracked female mallards nesting during 1998-2000 and located 318 nests in 6 types of land cover. Overall daily survival rate of nests was 0.945 AE 0.003 standard error (SE), corresponding to an estimated nest survival rate of 0.14. Hen success (i.e., the probability that an individual female will hatch a nest in one of her attempts) averaged 0.28 AE 0.03 SE. We used a model selection approach to examine covariates that might affect nest survival. Perimeter-to-area ratio (PAR) of the nest patch was the most important predictor of daily nest survival, with nest survival decreasing with increasing PAR. A greater percentage of nests hatched (18%) in habitats with low perimeter-to-area ratios (e.g., pastures, hayfields, Conservation Reserve Program fields, and managed grasslands) compared with habitats with high PAR (11%) such as drainage ditches, road-side ditches, fencerows, and waterways. Managing habitat in this region to increase mallard nest survival will be challenging, given the propensity of mallards to nest in linear habitats. If the climate change projections materialize in the 21st century, the southeastern portion of the Prairie Pothole Region could become a much more important breeding area for midcontinent mallards. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

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