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A DFA as you describe is called a separating DFA. There is some literature on this problem when $A$ and $B$ are regular languages, such as this paperLearning Minimal Separating DFA’s for Compositional Verification, by Yu-Fang Chen, Azadeh Farzan, Edmund M. Clarke, Yih-Kuen Tsay, Bow-Yaw Wang

Note that as @reinierpost states, without any restrictions on A and B, the problem may become undecidable.

A DFA as you describe is called a separating DFA. There is some literature on this problem when $A$ and $B$ are regular languages, such as this paper

Note that as @reinierpost states, without any restrictions on A and B, the problem may become undecidable.

A DFA as you describe is called a separating DFA. There is some literature on this problem when $A$ and $B$ are regular languages, such as Learning Minimal Separating DFA’s for Compositional Verification, by Yu-Fang Chen, Azadeh Farzan, Edmund M. Clarke, Yih-Kuen Tsay, Bow-Yaw Wang

Note that as @reinierpost states, without any restrictions on A and B, the problem may become undecidable.

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A DFA as you describe is called a separating DFA. There is some literature on this problem when $A$ and $B$ are regular languages, such as this paper

Note that as @Raphel@reinierpost states, without any restrictions on A and B, the problem may become undecidable.

A DFA as you describe is called a separating DFA. There is some literature on this problem when $A$ and $B$ are regular languages, such as this paper

Note that as @Raphel states, without any restrictions on A and B, the problem may become undecidable.

A DFA as you describe is called a separating DFA. There is some literature on this problem when $A$ and $B$ are regular languages, such as this paper

Note that as @reinierpost states, without any restrictions on A and B, the problem may become undecidable.

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A DFA as you describe is called a separating DFA. There is some literature on this problem when $A$ and $B$ are regular languages, such as this paper

Note that as @Raphel states, without any restrictions on A and B, the problem may become undecidable.