Michael Stephen Fiske

AEMEA Institute · Mathematics & Computational Science

Malware plays a key role in attacking critical infrastructure. With this problem in mind, we introduce systems that heal from a broader perspective than the standard digital computer model: Our goal in a more general theory is to be applicable to systems that contain subsystems that do not solely rely on the execution of register machine instructio...

Recent research has demonstrated electronic hardware attacks on pacemakers and insulin injectors. Injecting clock glitches can skip cryptographic instructions, defeating the security of the executing instructions. Typically, these attacks destabilize the dynamical behavior of the electronics. For over 70 years, flip-flops have been a fundamental b...

"Dynamical Systems that Heal” was awarded Best Paper at HICSS-56. Our primary contribution defines a principle of self-modifiability in dynamical systems and demonstrates how it can be used to heal a malfunctioning dynamical system. As far as we know, to date there has not been a mathematical notion of self-modifiability in dynamical systems; hit...

Malware plays a critical role in breaching computer systems. The computing behavior of a register machine program can be sabotaged, by making a very small change to the original, uninfected program. Stability has been studied extensively in dynamical systems and in engineering. Our primary contribution introduces a computing machine that is structu...

Malware plays a critical role in breaching computer systems. Cybersecurity research has primarily focused on malware detection. Detection methods are currently up against fundamental limits in theoretical computer science. The purpose of visual image authentication is to create Artificial Intelligence (AI) problems that are easy for humans to under...

A new computational model, called the ex-machine, executes standard instructions, meta instructions, and random instructions. Standard instructions behave similarly to machine instructions in a digital computer. Meta instructions self-modify the ex-machine’s program during its execution. We construct a countable set of ex-machines; each can compute...

Our goal is to construct mathematical operations that combine indeterminism measured from quantum randomness with computational determinism so that non-mechanistic behavior is preserved in the computation. Formally, some results about operations applied to computably enumerable (c.e.) and bi-immune sets are proven here, where the objective is for t...

Malware plays a significant role in breaching computer systems. Previous research has focused on malware detection even though detection is up against theoretical limits in computer science and current methods are inadequate in practice. We explain the susceptibility of computation to malware as a consequence of the instability of Turing and regist...

Physical implementations of digital computers began in the latter half of the 1930's and were first constructed from various forms of logic gates. Based on the prime numbers, we introduce prime clocks and prime clock sums, where the clocks utilize time and act as computational primitives instead of gates. The prime clocks generate an infinite abeli...

Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the first question, by introducing a new model called the ex-machine. The ex-machine executes Turing machine instru...

Physical implementations of digital computers began in the latter half of the 1930's and were first constructed from various forms of logic gates. Based on the prime numbers, we introduce prime clocks and prime clock sums, where the clocks utilize time and act as computational primitives instead of gates. The prime clocks generate an infinite abeli...

The notion of key generators is introduced to symmetric cryptography. Key generators help eliminate the dependence of a block cipher's security on a single, static key. If one of the dynamic keys is leaked to the adversary, then this compromise does not reveal future keys and prior keys used by the block cipher to encrypt distinct blocks of plainte...

In an embodiment, a secure module is provided that provides access keys to an unsecured system. In an embodiment, the secure module may generate passcodes and supply the passcodes to the unsecured system. In an embodiment, the access keys are sent to the unsecured system after the receiving the passcode from the unsecured system. In an embodiment,...

An active element machine is a new kind of computing machine. When implemented in hardware, the active element machine can execute multiple instructions simultaneously, because every one of its computing elements is active. This greatly enhances the computing speed. By executing a meta program whose instructions change the connections in a dynamic...

In [4], a computational procedure (Procedure 2) - combining quantum randomness and the active element machine (AEM) [5] - executes a universal Turing machine with Turing incomputable firing patterns. The procedure emulates any digital computer program so its computational steps are incomprehensible to an external observer. This procedure’s purpose...

The Turing machine is studied with new methods motivated by the notion of recurrence in classical dynamical systems theory. The state cycle of a Turing machine is introduced. It is proven that each consecutive repeating state cycle in a Turing machine determines a unique periodic configuration (point) and vice versa. This characterization is a peri...

A new computing machine, called an active element machine (AEM), and programming language is presented. This computing model is motivated by the positive aspects of dendritic integration, inspired by biology, and traditional programming lan-guages based on the register machine. Distinct from the traditional register machine, the fundamental computi...

New methods are presented for the machine recognition and learning of categories, patterns, and knowledge. A probabilistic machine learning algorithm is described that scales favorably to extremely large datasets, avoids local minima problems, and provides fast learning and recognition speeds. Templates may be created using an evolutionary algorith...

A new computing model, called the active element machine (AEM), is presented that demonstrates Turing incomputable computation using quantum random input. The AEM deterministically executes a universal Turing machine (UTM) program η with random active element firing patterns. These firing patterns are Turing incomputable when the AEM executes a UTM...

A new computing machine, called an active element machine (AEM), and programming language is presented. This computing model is motivated by the positive aspects of dendritic integration, inspired by biology, and traditional programming languages based on the register machine. Distinct from the traditional register machine, the fundamental computin...

This paper demonstrates a sequence of natural numbers that grows faster than any Turing computable function. This sequence is generated from a version of the tiling problem, called a coloring system. In our proof that generates the sequence, we use the notions of a chain and the unbounded sequence property, which resemble the methods of point set t...

We present new results about the dynamical behavior of Turing Machines. We define a transformation φ that creates a one-to-one correspondence from the Turing machine program rules to a finite set of two dimensional (x-y plane) affine maps, where the domain of each affine map is a distinct unit square. This transformation characterizes the computing...

Thesis (Ph. D., Mathematics)--Northwestern University, 1996.