Finding All Minimum-Size DFA Consistent with Given Examples: SAT-Based Approach

Deterministic finite automaton (DFA) is a fundamental concept in the theory of computation. The NP-hard DFA identification problem can be efficiently solved by translation to the Boolean satisfiability problem (SAT). Previously we developed a technique to reduce the problem search space by enforcing DFA states to be enumerated in breadth-first search (BFS) order. We proposed symmetry breaking predicates, which can be added to Boolean formulae representing various automata identification problems. In this paper we continue the study of SAT-based approaches. First, we propose new predicates based on depth-first search order. Second, we present three methods to identify all non-isomorphic automata of the minimum size instead of just one—the Open image in new window P-complete problem which has not been solved before. Third, we revisited our implementation of the BFS-based approach and conducted new evaluation experiments. It occurs that BFS-based approach outperforms all other exact algorithms for DFA identification and can be effectively applied for finding all solutions of the problem.