AG asked: does randomness imply no-FTL-signaling?

Let me ask: does determinism imply FTL-signaling?

A is one of the two wings of a Bell apparatus
i is the observable to be measured in A
x is the possible value of i
B is the other wing of a Bell apparatus
j is the observable to be measured in B
y is  the possible value of j
Lambda are hidden variables
p are probabilities

If we write
p_[A,Lambda] (x|i,j) = p_[A,Lambda] (x|i)
p_[B,Lambda] (y|i,j) = p_[B,Lambda] (y|j)
the above is a sort of "locality" condition,
since the value x only depends on the observable i,
and the value y only depends on the observable j.

In a (hypothetical 
https://www.google.com/search?client=firefox-b-d&sxsrf=ALeKk02Cur06my_H17d_9fUXbVDqBH5ESQ:1608715874782&q=hypothetical&spell=1&sa=X&ved=2ahUKEwiAy4rS5ePtAhXLO-wKHWX6DTYQkeECKAB6BAgEEDU
 ) deterministic theory (but reproducing QM)
the above "locality" condition is violated.

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