The strongest logical correlation is −0.5, the lower the better.
For p and sim(p), the logical correlation would be −ε, assuming that p and sim(p) have the same output. This is a pretty strong logical correlation.
This is because equal output guarantees a logical correlation of at most 0, and one can then improve the logical correlation by also having similar traces. If the outputs have string distance 1, then the smallest logical correlation can be only 0.5.
The strongest logical correlation is −0.5, the lower the better.
For p and sim(p), the logical correlation would be −ε, assuming that p and sim(p) have the same output. This is a pretty strong logical correlation.
This is because equal output guarantees a logical correlation of at most 0, and one can then improve the logical correlation by also having similar traces. If the outputs have string distance 1, then the smallest logical correlation can be only 0.5.