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Following the impressive progress made in the quest for efficient SAT solving in the last years, a number of researches has focused on explaining performances observed on typical application problems. However, until now, tentative explanations were only partial, essentially because the semantic of the original problem was lost in the translation to SAT. In this work, we study the behavior of so called “modern” SAT solvers under the prism of the first successful application of CDCL solvers, i.e., Bounded Model Checking. We trace the origin of each variable w.r.t. its unrolling depth, and show a surprising relationship between these time steps and the communities found in the CNF encoding. We also show how the VSIDS heuristic, the resolution engine, and the learning mechanism interact with the unrolling steps. Additionally, we show that the Literal Block Distance (LBD), used to identify good learnt clauses, is related to this measure. Our work shows that communities identify strong dependencies among the variables of different time steps, revealing a structure that arises when unrolling the problem, and which seems to be caught by the LBD measure., QC 20170919

© The Author(s), 2013. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Climate of the Past 9 (2013): 1111-1140, doi:10.5194/cp-9-1111-2013., Both historical and idealized climate model experiments are performed with a variety of Earth system models of intermediate complexity (EMICs) as part of a community contribution to the Intergovernmental Panel on Climate Change Fifth Assessment Report. Historical simulations start at 850 CE and continue through to 2005. The standard simulations include changes in forcing from solar luminosity, Earth's orbital configuration, CO2, additional greenhouse gases, land use, and sulphate and volcanic aerosols. In spite of very different modelled pre-industrial global surface air temperatures, overall 20th century trends in surface air temperature and carbon uptake are reasonably well simulated when compared to observed trends. Land carbon fluxes show much more variation between models than ocean carbon fluxes, and recent land fluxes appear to be slightly underestimated. It is possible that recent modelled climate trends or climate–carbon feedbacks are overestimated resulting in too much land carbon loss or that carbon uptake due to CO2 and/or nitrogen fertilization is underestimated. Several one thousand year long, idealized, 2 × and 4 × CO2 experiments are used to quantify standard model characteristics, including transient and equilibrium climate sensitivities, and climate–carbon feedbacks. The values from EMICs generally fall within the range given by general circulation models. Seven additional historical simulations, each including a single specified forcing, are used to assess the contributions of different climate forcings to the overall climate and carbon cycle response. The response of surface air temperature is the linear sum of the individual forcings, while the carbon cycle response shows a non-linear interaction between land-use change and CO2 forcings for some models. Finally, the preindustrial portions of the last millennium simulations are used to assess historical model carbon-climate feedbacks. Given the specified forcing, there is a tendency for the EMICs