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A search for CP violation in the phase-space structures of D0 and D0bardecays to the final states K-K+pi-pi+ and pi-pi+pi+pi- is presented. The searchis carried out with a data set corresponding to an integrated luminosity of1.0fb^-1 collected in 2011 by the LHCb experiment in $pp$ collisions at acentre-of-mass energy of 7TeV. For the K-K+pi-pi+ final state, the four-bodyphase space is divided into 32 bins, each bin with approximately 1800 decays.The p-value under the hypothesis of no CP violation is 9.1%, and in no bin is aCP asymmetry greater than 6.5% observed. The phase space of the pi-pi+pi+pi-final state is partitioned into 128 bins, each bin with approximately 2500decays. The $p$-value under the hypothesis of no CP violation is 41%, and in nobin is a CP asymmetry greater than 5.5% observed. All results are consistentwith the hypothesis of no CP violation at the current sensitivity.

Model-independent search for CP violation in D0 to K-K+pi-pi+ and D0 to pi-pi+pi+pi- decays