NARS does have a finite set of possible final states, though, because it's implemented on a finite-state machine...
And, given a NARS codebase and its state in RAM & on disk at a given point in time, you CAN predict its behavior from its inputs alone... ben > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]]On > Behalf Of Pei Wang > Sent: Sunday, January 12, 2003 11:05 AM > To: [EMAIL PROTECTED] > Subject: Re: [agi] AI and computation (was: The Next Wave) > > > James, > > I basically agree with your points. > > In my replies to Shane and Ben, I argued that the TM definition is too > limited by assuming a unique initial state. Now your posting addressed > another related topic: the final state. In my paper I said that > my system is > not a TM, also because it doesn't have a set of predetermined final states > where the system report a final answer and stop. Instead, my > system reports > the best answers it finds so far, and continue to looking for better > answers. When it stop working on a problem, it is not because it > is "solved" > (or proven to be unsolvable), but because the system has no > resource for it. > In this way, the traditional halting problem and scalability problem don't > exist anymore, though it doesn't mean that the system can solve > all problems > efficiently. Instead, it means that the system's behavior cannot be > predicted from the current problem alone. > > I'm afraid I just opened another can of worm. > > Pei > > ----- Original Message ----- > From: "James Rogers" <[EMAIL PROTECTED]> > To: <[EMAIL PROTECTED]> > Sent: Sunday, January 12, 2003 12:26 AM > Subject: Re: [agi] AI and computation (was: The Next Wave) > > > > On 1/11/03 5:31 PM, "Pei Wang" <[EMAIL PROTECTED]> wrote: > > > > > > My argument, briefly speaking, is that it is quite possible, in the > current > > > computer, to solve problems in such a way that is non-deterministic > (i.e., > > > context-sensitive) and open-ended (as in anytime algorithms). Such a > > > process doesn't satisfy the definition of computation, > doesn't follow a > > > predetermined algorithm, and has no fixed complexity. > > > > > > Interesting, as I make a similar argument. I'm using an unconventional > > model of universal computation on finite state machinery that, > among other > > things, exhibits these properties. I would say that it is less that > > computational theory doesn't apply than it is a matter of people making > > assumptions about the underlying nature of the machine when > they apply it. > > > > For example, in our system it is quite possible for an > iterative algorithm > > implemented on our machinery to get rewritten as its executing in a > > particular context such that it completes itself in an "unexpected" > manner. > > In this case, "rewritten" is much deeper than simple > self-modifying code; > > there is literally no distinction between code, data, and the machinery > > itself, so strange things can happen. Normal computational analysis > > generally assumes that at the very least the machinery is static, if not > the > > code, but that is not the case here. The very concept of "algorithm" as > > normally used makes certain implicit assumptions about the fundamental > > nature of the machinery it is running on, whether valid or not. > Standard > > computational analysis could be done on our machinery, it would just be > very > > different. > > > > > > Note that this particular property is more-or-less how our system cheats > the > > halting problem, infinite loops, and similar. When you run an program > > instance that ends up in this state, the algorithms (in a generic sense) > > tend to rewrite themselves such that they jump to a conclusion and > > terminate. However, this is not so much a property of the algorithm but > the > > nature of the universal computing machinery you are running it on. The > very > > machinery itself is deeply probabilistic and non-axiomatic, so > there is no > > guarantee that an algorithm will run in an expected manner every time > > ("expected" in the sense of the conventional model of universal > computers -- > > obviously I know this will happen). "Here be monsters..." > > > > > > > > > For that "level" issue, one way to see it is through the concept of > "virtual > > > machine". We all know that at a low level computer only has > procedural > > > language and binary data, but at a high level it has non-procedural > language > > > (such as functional or logical languages) and decimal data. > Therefore, > if > > > virtual machine M1 is implemented by virtual machine M2, the two may > still > > > have quite different properties. What I'm trying to do is to > implement > a > > > "non-computing" system on a computing one. > > > > > > I know exactly what you are talking about here, though I don't know if > > everyone will get it; I've had to explain this to others before (and > > demonstrate it too). We implement a virtual machine on top of > a standard > > computer architecture that is designed around a fundamentally different > > model of a universal computer. > > > > One of the demonstrations that never fails to impress is that we can run > > classes of algorithms with well-known complexity profiles > (typically ones > > with intractable scalability characteristics), and then run the same > > algorithms on the virtual machine and get results that conventional > analysis > > suggests should be effectively impossible on that same hardware. (Note: > > Only certain classes of algorithms exhibit this characteristic on our > > virtual machine, so naturally those are the ones we choose and > fortunately > > they tend to be "interesting" algorithms.) The problem is that most > > conventional analytical computational theory typically makes many > > assumptions about the behavior and nature of the universal > computer (e.g. > > that it is fundamentally a zero-order machine) that do not apply to our > > virtual machine. The virtual machine is still bound by the same laws of > > computational theory that everyone else is, but the effective mechanisms > of > > computation are very different from the norm and you have to do your > > analysis with a different set of assumptions to get useful results. > > > > At the same time, I would note that our virtual machine is substantially > > worse at doing some types of computation that conventional universal > > computation architectures do very well, so there is something of a > > trade-off. > > > > To put it another way, it is possible to write a universal > virtual machine > > that runs on standard silicon that is not itself reducible to silicon > using > > any existing electronics technology (though in theory it might > be possible > > with, say, some molecular computer technology that doesn't exist yet). > > > > > > -James Rogers > > [EMAIL PROTECTED] > > > > ------- > > To unsubscribe, change your address, or temporarily deactivate your > subscription, > > please go to http://v2.listbox.com/member/?[EMAIL PROTECTED] > > > ------- > To unsubscribe, change your address, or temporarily deactivate > your subscription, > please go to http://v2.listbox.com/member/?[EMAIL PROTECTED] > ------- To unsubscribe, change your address, or temporarily deactivate your subscription, please go to http://v2.listbox.com/member/?[EMAIL PROTECTED]
