Dynamic programming is used to find periodic proton conduction paths in pseudo-cubic and orthorhombic perovskites. Periodic paths through a large periodic simulation box are compared to periodic paths through a smaller simulation box and pathways stitched from small simulation box periodic and aperiodic paths. For both size systems in the 900-1300 K temperature range, overall average limiting barriers over the N-step periodic pathways considered are 0.3, 0.4, and 0.6 eV for BaZr0.875Y0.125O3 , SrZr0.875Y0.125O3 and SrZr0.875-Al0.125O3, respectively, in good relative agreement with earlier experiments. However, differences in the ensemble weighted fraction of rotation, intraoctahedral transfer, and interoctahedral transfer limiting steps highlights differences in the small and large system periodic path ensembles. In contrast, the averages over the stitched ensemble are in excellent agreement with the large system averages. This suggests that a careful combining of small system pathways can yield pathways representative of a large system. (c) 2011 Elsevier B.V. All rights reserved.