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In this paper we propose an automated verification approach to checking intransitive noninterference for deterministic finite state systems. Our approach is based on the counterexamples search verification strategy, and is conducted in gradual manner. It produces counterexamples of minimal length. Further, we reduce the counterexamples search to propositional satisfiability. For the case that there are no counterexamples, we also introduce the window induction proof method in order to avoid considering unnecessary iterations, and show that the induction proof can be performed by the boolean decision procedure. In addition, based on graph-theoretic properties of systems we propose an over-approximation to the length of the smallest counterexample, and the over-approximation can also be checked by the boolean decision procedure.

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