[Caml-list] Invitation to work on projects

[Kenneth Adam Miller <kennethadammiller@gmail.com>]

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Hello all,

I am coming to a phase in my life where I won't be a researcher anymore and
would like to open up my line of project ideas and objectives to those who
are interested to learn more or work together on. If you see a title of
some work you are interested in please send me a message so we can discuss
it on the mailing list. Some of my project ideas are strictly white papers,
some of them are very complex software research projects. I'm not going to
state the internals of all projects but for many of them I have some
inclination on how to proceed in implementation. I'll make an exception to
this for a couple of them so that you can get a glimpse of the insides of
such projects though. For most of these, they are covered by a statement of
purpose I wrote when applying to IUPUI. So I will paste that below (I'm too
lazy to rewrite it).

(These two projects are the top two I have prioritized, so I'm describing
their internals here).

Machine Learning Induction (both a white paper and a software project)-
Using an anthology of functions implemented as an enumeration of all
possible semantic sequences to generate C fragments from lisp, we train a
model on induction that reasons about code inductively.

Compiling an Inverse Compiler (both a white paper and a software project) -
There are three parts to this massive project. The first is a compiler
plugin that promotes every CPU operation to a matrix representation that is
invertible, and produces functions that compute an input given an output by
inverting all operations and computing in reverse. The second part is a
function anthology to exercise all possible semantic sequences up to a
finite size limit: by building this anthology we can learn what inputs
(source) map to what outputs (binary). The last part is compiling a
compiler using the new plugin to produce an inverse compiler that accepts
as input a binary and produces a source code as output.

IUPUI Math Statement of Purpose Kenneth Adam Miller

I hope to develop practice in mathematical rigor with an education from
IUPUI, to learn and do research for the rest of my life. Assisting other
researchers with their goals is fulfilling, and I am especially excited to
work in the area of modern analysis, mathematical physics, and dynamical
systems. Authoring a textbook, The Fractal Nature of Time, targeting
quantum algorithms and fractal mathematics for synthesis, is a life goal.
The objective of this textbook will be to transform the way programming
languages are conceived to suit the capabilities of quantum computers
better, to synthesize algorithms using the quantum computer, to introduce
new formal methods, and to deeply change the way that computation is
defined. Most importantly, I hope to relate recursion and dimension in this
textbook, providing a more succinct, rigorous yet powerfully expressive
lambda calculi to transform math of the quantum computational model.

I have extensive experience with numerous languages, including OCaml, Rust,
C, C++, Python, Go, Coq, Matlab and Java. Completed projects include LLVM &
BAP analysis passes and plugins, parallel/concurrent programming, kernel
drivers, embedded development, reverse engineering, software rewriting and
instrumentation, binary exploit development, and even quantum analyses for
vulnerability identification. I work very hard and have a creative flair
for introducing simplicity in programming solutions. Though I have a
computer science background, I have always loved mathematics and struggled
to pick between the two. The ideals of mathematics serve in formalizing and
curating solutions to problems in quantum computing. Both are important, as
using machines to assist in my computations enables orders of magnitude
more mathematics to be explored.

Synthesis with quantum algorithms should strive to produce Turing complete
output. I argue for new directions to address outstanding limitations. The
scalability of computing non-trivial operators may be alleviated by
computationally exploring matrix patterns that leverage entrancy and
periodicity. The tractability of encoding data into superpositions and
number of gates per qubit may be better approached using iterated function
systems to transform the problem. The quantum computational model does not
capture the entire narrative, but a careful rigorization using new fractal
numeric properties may serve to more precisely relate between
spatio-temporal eventualities, recursion and dimension. Representation
within a superposition is challenging semantically, in the properties
produced by each eventuality, and for the types within, but this can be
addressed with an extended isomorphy. Knowing which of the potential
algorithms are efficient is challenging, but there should exist
isomorphisms allowing to evaluate functions over transforming structural
product spaces sufficient to reveal a fast option in a particular
dimension. Completeness and consistency concerns would remain deeply vexing
but I believe an upgraded Godel encoding is achievable by replacing primes
with new numeric mechanisms for recognizing orthogonality, while also
yielding more precise statements governing the measure of these concerns.

In conclusion, without the practice to hone my writing and research, the
potential to pursue these works would be lost. IUPUI is therefore vital to
me. I am happy to learn more about the specific interests of fellow
researchers, and hope that my work eventually will enable algorithms to
scale as quantum computers grow.

Subjects I hope to write on:

  A Quantum Algorithm for Synthesizing Algorithms

Fractally Self Synthesizing Language

Mathematical Properties of Love

An (Extended Curry-Howard) Isomorphism for Quantum Computation

A Fractal Lambda Calculus

Native Quantum Languages

Shortfalls of the Quantum Computational Model

Quantum Zero-Knowledge Proof Search

Quantum Computing and the Riemann Hypothesis

Varied Uses of Deutsch-Josca Algorithm

Mathematical Property Representation by Palindrome Features

Quantum Algorithms and Fixpoints

A Quantum Algorithmic Method for Identifying Lowest Complexity

Quantum Algorithms for Vulnerability Analyses

Synthetic Charisma

Compiler Instrumentation and Algorithms for Language Acquisition

Mathematical Limitations of Many Binary Analysis Tasks

Quantum Parallelism and Complexity

Bitcoin is a Cryptographic Attack

The Blockchain and Fractal Mathematics

Simple Ground Truth Mechanisms for Binary Analysis Tasks

The Fundamental Theorem of Computer Science

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