The parallelism theorem of labeled transition systems is, I think, misinterpreted sometimes. It's too strong to claim that for any parallel process a sequential process can be defined that operates/funtcions the same way. The theorem relies on the existence of hidden transitions within the parallel process that don't need to be in the sequential process. So, it's better to say:
For any given parallel process where the set of observables is smaller than the set of all its states and transitions, a sequential process can be defined that has the same observable states and transitions. I.e. for any given parallel process, a sequential one can be defined that SIMULATES it. This is a core simulation principle and it's why systems engineers focus so much on validation, matching observables between the simulation and its referent. I'm not arguing that parallelism is sufficient for machines that construct themselves. As I pointed out in the other thread, we still have deadlock (which is the computer equivalent of Rosen's primary objection). I'm just arguing that the parallelism theorem is not the right formal tool to show why parallelism is insufficient. On 10/27/18 5:20 AM, John Kennison wrote: > I think that Rosen is right in saying that having a parallel machine (in > which various operations happen simultaneously) will not do the trick because > given any parallel machine one can define a sequential machine that functions > in the same way. -- ∄ uǝʃƃ ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
