Fwd: continuous Turing machines

[YKY (Yan King Yin, 甄景贤)]

The idea:  make programs continuous and then evolve programs using continuous techniques.  Valiant's recent book "Probably Approximately Correct" has said something about evolving continuous parameters for strong AI.  (It may be more tractable than evolving programs with discrete elements, the kind of programs we have known usually).

In the context of logic-based AI (such as OpenCog, NARS, and my Genifer) the idea is to make all logic and procedural statements continuous.  The part concerning making logic continuous is via algebraization which I have been looking into, but will discuss elsewhere.  The "procedural" aspect can be realized by letting the AGI control a Turing machine (TM) with one or more tapes, and by making such a Turing machine "continuous".

As a first step towards continuous TMs, we can start with finite state machines (FSM).  It seems that a continuous version of FSMs corresponds to continuous dynamical systems (aka topological dynamical systems).  I have not looked into the details of this correspondence, but it looks fairly straightforward.

To make TMs continuous is somewhat more difficult.  One way is to turn the "tape read/write operations" into states of an FSM (in such case the number of states may become infinite).  But I'm not sure if that is a good way to create continuous TMs.

Any other idea for continuous TMs?

Thanks in advance =)

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YKY

"The ultimate goal of mathematics is to eliminate any need for intelligent thought" -- Alfred North Whitehead