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Since it has been found that the MadGraph Monte Carlo generator offers superior flavour-matching capability as compared to Alpgen, the suitability of MadGraph for the generation of ttb¯ ¯b events is explored, with a view to simulating this background in searches for the Standard Model Higgs production and decay process ttH, H ¯ → b ¯b. Comparisons are performed between the output of MadGraph and that of Alpgen, showing that satisfactory agreement in their predictions can be obtained with the appropriate generator settings. A search for the Standard Model Higgs boson, produced in association with the top quark and decaying into a b ¯b pair, using 20.3 fb−1 of 8 TeV collision data collected in 2012 by the ATLAS experiment at CERN’s Large Hadron Collider, is presented. The GlaNtp analysis framework, together with the RooFit package and associated software, are used to obtain an expected 95% confidence-level limit of 4.2 +4.1 −2.0 times the Standard Model expectation, and the corresponding observed limit is found to be 5.9; this is within experimental uncertainty of the published result of the analysis performed by the ATLAS collaboration. A search for a heavy charged Higgs boson of mass mH± in the range 200 ≤ mH± /GeV ≤ 600, where the Higgs mediates the five-flavour beyond-theStandard-Model physics process gb → tH± → ttb, with one top quark decaying leptonically and the other decaying hadronically, is presented, using the 20.3 fb−1 8 TeV ATLAS data set. Upper limits on the product of the production cross-section and the branching ratio of the H± boson are computed for six mass points, and these are found to be compatible within experimental uncertainty with those obtained by the corresponding published ATLAS analysis.