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Transition nets and Markov chains

  1. May 8, 2009 #1
    Has anyone here done any study with automata?

    i'm interested in deriving a general model, in a state + transition encoded way; that's a parsing grammnar approach to start with, then generalize it further to a sort of wavevector/wavefunction algebra; a QM model since I study QI at the mo.
    IS needs QM reps that are/are not crammed with complicated "machine instructions" - we need better abstractions of 0,1 in 3 and 2 dimensions. Hall liquids and the AB effect essentially encode these "new" algebras. :)
  2. jcsd
  3. May 9, 2009 #2
    Hm. OK; The fundamental principle of information is that: there isn't any if time and space are not real, for any signal s(t). Or, there is no physical way to communicate in zero time, or over any distance unless energy is transferred (as information, spatially encoded in time for signal s).

    So that: Temporal + spatial displacements extend (as communications) to surfaces where they are transported, copied/erased, and polarized. There would be no possibility of computation without communication, so that Shannon's "information principle", is that information requires a physical medium or circuit, and spatial extent in time.

    Essentially a binary computer is a set of 2-dimensional gates in, or on a manifold M; linear transformations of 'information' (bits of stored charge) in registers which are extensions of 2n bits, or w bits wide, therefore represent a time-independent algebra A, for the manifold M|(s,t), and velocities are of 'logic' as a path for a computation through a number n-1 of registers, where the 1st is the 'input' and the last or nth is the 'output'.

    Computational flow is independent of the physical realization of the logic that 'runs' any process; since two different physical computers can determine the same result, but in different amounts of time. Here 'time' is a background-independence; we can build machines that 'compute' physically in indeterminate time, because Brownian motion is the physical 'force' acting on the flow in logical terms.
    We might not want to wait centuries or millions of years, but the Brownian machine will give as good or accurate a result as we like - it's a question of design.

    We like answers in shorter amounts of time, or polynomial time. P-time rules the C-space, there is no way to determine that a 'program' will take a given path, and halt with the "correct answer"; however, it always has one, even if it's not what was expected.

    A machine which is digitized "uses" - u uses v - charge (in electrons) as the deformed potential. Spin or magnetic interactions are overwhelmed by the geometry - there are no inductive currents, except for stray ones. If information is written in another, external form, then magnetic effects can be used to transform the computational and physical basis.

    There is a difference; in electronic machines the two are always assumed to be congruent, but this isn't the case in quantum circuits since you only get a result when you perturb the system. Preparing a circuit is equivalent to running an algorithm, the recovery means adjusting the phase of a state so a preserved phase-difference evolves as a pure state.
    This is what happens in polarization - sunglasses absorb 1/2 the "glare" = incident light polarized the 'wrong way', and delivers a remainder in parallel mode to you, or to your vision. You are in the quantum world when you wear them, since removing the filters means you see classical glare (yep, still there). The filters process photons either singly or as a group - it doesn't matter because you see the result 'now', not when the glasses actually do anything.

    Flow is linear because of the register path, but thermodynamic interference might mean a halt occurs even though the process is evolving to a result. In an electronic/thermodynamic system the interference is unimportant for a temperature within a certain physical limit; so that classical machines are restricted to polynomial time processing by temperature and the physical basis.

    The sum + product logic of digital machines means that flow occurs because Boole products remove or erase something, summation doesn't. In that sense summation (OR,XOR) is a diffusion, production (AND) is a dispersion. The first is expansive, the second linear and closed/open for some path through a register map B(x), then M(x')|n> -> M(x)|i> + B|i>; or "output = input x + map B over x(i)". The index i counts up to n-1 and the result is in M(x) after n steps of P-time.

    An input x(n) is transformed into a result by M(x) which is a computation C(x)|i> where products make potential (logic) vanish or get absorbed by the path taken, since AND loses one bit per 2-d switch, only one input can be recovered or recalled as the one that 'threw' the switch, the other is lost irrecoverably. AND is not therefore affine but required for logical flow in any M that computes information, by communicating it.
    Last edited: May 9, 2009
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