It was shown before that the NP-hard problem of deterministic finite automata (DFA) identification can be effectively translated to Boolean satisfiability (SAT). Modern SAT-solvers can tackle hard DFA identification instances efficiently. We present a technique to reduce the problem search space by enforcing an enumeration of DFA states in depth-first search (DFS) or breadth-first search (BFS) order. We propose symmetry breaking predicates, which can be added to Boolean formulae representing

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... ious DFA identification problems. We show how to apply this technique to DFA identification from both noiseless and noisy data. Also we propose a method to identify all automata of the desired size. The proposed approach outperforms the current state-of-the-art DFASAT method for DFA identification from noiseless data. A big advantage of the proposed approach is that it allows to determine exactly the existence or non-existence of a solution of the noisy DFA identification problem unlike metaheuristic approaches such as genetic algorithms.