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Processing personal data is regulated in Europe by the General Data Protection Regulation (GDPR) through data processing agreements (DPAs). Checking the compliance of DPAs contributes to the compliance verification of software systems as DPAs are an important source of requirements for software development involving the processing of personal data. However, manually checking whether a given DPA complies with GDPR is challenging as it requires significant time and effort for understanding and identifying DPA-relevant compliance requirements in GDPR and then verifying these requirements in the DPA. In this paper, we propose an automated solution to check the compliance of a given DPA against GDPR. In close interaction with legal experts, we first built two artifacts: (i) the "shall" requirements extracted from the GDPR provisions relevant to DPA compliance and (ii) a glossary table defining the legal concepts in the requirements. Then, we developed an automated solution that leverages natural language processing (NLP) technologies to check the compliance of a given DPA against these "shall" requirements. Specifically, our approach automatically generates phrasal-level representations for the textual content of the DPA and compares it against predefined representations of the "shall" requirements. Over a dataset of 30 actual DPAs, the approach correctly finds 618 out of 750 genuine violations while raising 76 false violations, and further correctly identifies 524 satisfied requirements. The approach has thus an average precision of 89.1%, a recall of 82.4%, and an accuracy of 84.6%. Compared to a baseline that relies on off-the-shelf NLP tools, our approach provides an average accuracy gain of ~20 percentage points. The accuracy of our approach can be improved to ~94% with limited manual verification effort.