While there are real use cases for the above, if you are looking at bloom filters make sure you check the above works for your need. First-order with least fix

While there are real use cases for the above, if you are looking at bloom filters make sure you check the above works for your need. First-order with least fixed point FO(LFP) == P As P=co-P but we think NP!=co-NP, bloom filters often have value for access to a small and fast path to co-NP In that case the collisions don't matter because often excluding membership is more valuable than proving membership and you have to choose one. That is why outlook used it to reduce address completion, even if a hit requires the expensive call to the server, the set of email addresses not in your address book is far larger. But it is all horses for courses. If your need does fit in P you have a lot of options, while the options for co-NP is far more rarified.