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