give example of 2 languages A and B such that A and B are undecidable but there concatenation A.B is decidable.
closed as too localized by Andreas Blass, Andres Caicedo, Mark Sapir, Henry Cohn, Benjamin Steinberg Apr 30 '12 at 2:33
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Let $A$ contain all even-length strings, plus an undecidable collection of odd-length strings. Let $B$ contain all odd-length strings, plus the empty string, plus an undecidable collection of even-length strings. So each is undecidable, but the concatenation $AB$ consists of all strings and hence is decidable.