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.
KeywordsGrammatical inference Automata identification Symmetry breaking Boolean satisfiability
The authors would like to thank Igor Buzhinsky, Daniil Chivilikhin, Maxim Buzdalov for useful comments. This work was financially supported by the Government of Russian Federation, Grant 074-U01.
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