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This paper presents the implementation of a self-replicating finite-state machine (FSM) and a self-replicating Turing Machine (TM) using bio-inspired mechanisms. Building on previous work that introduced self-replicating structures capable…
Quantum computing is a new model of computation, based on quantum physics. Quantum computers can be exponentially faster than conventional computers for problems such as factoring. Besides full-scale quantum computers, more restricted…
The {\em diagonalization technique} was invented by Georg Cantor to show that there are more real numbers than algebraic numbers and is very crucial in {\em theoretical computer science}. In this work, we enumerate all of the…
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
A universal Turing machine is a powerful concept - a single device can compute any function that is computable. A universal spin model, similarly, is a class of physical systems whose low energy behavior simulates that of any spin system.…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Topic modelling was mostly dominated by Bayesian graphical models during the last decade. With the rise of transformers in Natural Language Processing, however, several successful models that rely on straightforward clustering approaches in…
According to Deutsch, a universal quantum Turing machine (UQTM) is able to perform, in repeating a fixed unitary transformation on the total system, an arbitrary unitary transformation on an arbitrary data state, by including a program as…
Traditional Turing machines are semantically poor, they only concern the syntactic manipulation of symbols, discarding the mathematical semantics behind the symbols. This semantic deficiency is considered the root cause of the three major…
Expanding upon the widely recognized notion of mathematical universality in Turing machines, a concept of thermodynamic universality in Turing machines is introduced. Under the physical Church-Turing thesis, the existence of a…
Nonlinear monotone transformations are used extensively in normalizing flows to construct invertible triangular mappings from simple distributions to complex ones. In existing literature, monotonicity is usually enforced by restricting…
Due to the limitation on computational power of existing computers, the polynomial time does not works for identifying the tractable problems in big data computing. This paper adopts the sublinear time as the new tractable standard to…
This paper analyzes infinitary nondeterministic computability theory. The main result is D $\ne$ ND $\cap$ coND where D is the class of sets decidable by infinite time Turing machines and ND is the class of sets recognizable by a…
The enormous energy demand of artificial intelligence is driving the development of alternative hardware for deep learning. Physical neural networks try to exploit physical systems to perform machine learning more efficiently. In…
Networks of coupled nonlinear optical resonators have emerged as an important class of systems in ultrafast optical science, enabling richer and more complex nonlinear dynamics compared to their single-resonator or travelling-wave…
The complexity class $NP$ can be logically characterized both through existential second order logic $SO\exists$, as proven by Fagin, and through simulating a Turing machine via the satisfiability problem of propositional logic SAT, as…
Nanomechanical computers promise a greatly improved energetic efficiency compared to their electrical counterparts. However, progress towards this goal is hindered by a lack of modular components, such as logic gates or transistors, and…
Harnessing the intrinsic dynamics of physical systems for information processing opens new avenues for computation embodied in matter. Using simulations of a model system, we show that assemblies of DNA tiles capable of self-organizing into…
When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions bear on the question. Modern computer algebra algorithms can…