The Phase of the “1” - Brain Theory from a Circuits and Systems Perspective - page 171

Fundamental to multivibrator functions are h-transforms, introduced above, that
permit an ability to distinguish the state 1] 0 after

sampling. With the help of such transforms it was shown that a given but unknown
multivibrator function in the symmetric and antisymmetric class may be classified
conveniently.
For one simulated qubit, n

[1 1] 0 from the state η η [1

1, symmetric and antisymmetric includes constant
functions with output fixed at 0 or 1, and nonconstant functions (inverters and
buffers). In general, for symmetric and antisymmetric functions involving n
simulated qubits, for n

¼

> 0, a single readout is enough to classify the multivibrator
function (normally up to 2 n evaluations of a given but unknown binary function
would be necessary).
A multivibrator function is identified to within a complement, since
complements cannot be distinguished. For example, the functions “0110” and
“1001” are complements, but give the same sampled readout using the above
transforms.
An interesting concept is a transformation that will help to identify what satisfies
a given multivibrator function. Of special interest is a decoding function. This is a
multivibrator function in which one of the outcomes is tagged with a negative sign
(in probability space).
If the multivibrator function is sophisticated, it will be far from obvious what
satisfies it. For example, there are Boolean equations that serve to define the
prime factors of a large integer. Using brute force, it could take many trials to
discover what satisfies such equations, since a great many prime numbers would
have to be tested. But if such a function is implemented as a multivibrator
function on simulated qubits, what satisfies it may be found using relatively
few operations.
A decoding function, after suitable transformation, needs to be evaluated
roughly 2 n/2 times. Ordinarily it would require up to 2 n evaluations to find what
satisfies it. So there are significant advantages to multivibrator functions for larger
n, when working on satisfiability problems.
A simulated qubit can encode a great deal of additional information in its
frequency and phase. For example, by varying frequency, simulated qubits can
store true, false, and true/false simultaneously. Advantages are easy to demonstrate
on paper. Using binary combinations of [1 0], [0 1], and [1 1], the number of codes

that can be stored increases exponentially with n and is far more than a mere 2 n ,
which is all that n bits provide.
Memory is important, so options for increasing memory density cannot be
dismissed without due consideration. The above multivibrator function identifi-
cation methods and the above multivibrator function satisfiability methods are
interesting to study, and they mightbediscoveredtohavearoletoplay
biologically.

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