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The configuration of firewalls is highly error prone and automated solution are needed in order to analyze its correctness. We propose a formal and automatic method for checking whether a firewall reacts correctly with respect to a security policy given in an high level declarative language. When errors are detected, some feedback is returned to the user in order to correct the firewall configuration. Furthermore, the procedure verifies that no conflicts exist within the security policy. We show that our method is both correct and complete. Finally, it has been implemented in a prototype of verifier based on a satisfiability solver modulo theories (SMT). Experiment conducted on relevant case studies demonstrate the efficiency and scalability of the approach.