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A firewall is the core of a well defined network security policy. This paper presents an automata-based method to study firewall security policies. We first propose a procedure that synthesizes an automaton that describes a security policy given as a table of rules. The synthesis procedure is then used to develop procedures to detect: incompleteness, anomalies and discrepancies in security policies. A method is developed to represent the automaton by a policy qualified as mixable and that has practical utilities, such as ease to determine the whitelist and the blacklist of the policy. The developed procedures have been deeply evaluated in terms of time and space complexities. Then, a real case study has been investigated. The obtained results confirm that the developed procedures have reasonable complexities and that their actual execution times are of the order of seconds. Finally, proofs of all results are provided.