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The present paper is interested in the following decision problems: (1) given finite frames F, F^', determine if there exists a frame F^'' such that F and F^'@?F^'', the synchronous product of F^' and F^'', are bisimilar; (2) given finite frames F, F^', determine if there exists a frame F^'' such that F and F^'@?F^'', the asynchronous product of F^' and F^'', are bisimilar. It shows that variants of the filtration method are adequate for solving them.