On Wed, Jul 10, 2024 at 10:24:52AM -0400, Jason Resch wrote: > > There was a study done in the 1950s on probabilistic Turing machines ( > https:// > www.degruyter.com/document/doi/10.1515/9781400882618-010/html?lang=en ) that > found what they could compute is no different than what a deterministic Turing > machine can compute.
But it would appear that computational complexity classes do differ. I seemed to remember that P=NP for Turing machines with random oracles, but it would seem (https://en.wikipedia.org/wiki/Random_oracle) that whilst there does exist an oracle for which P=NP (Baker-Gill-Solovay theorem), for random oracles generally, P≠NP with probability 1, ie P=NP is only true on a set of measure zero of random oracles. Let me know if I've misinterpreted that stuff... Seems important, as evolution is a computational process with a random oracle, and it does appear to be remarkably effective at solving (at least heuristically) computationally hard problems. Cheers -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/20240720023944.GA15533%40zen.
