Turing machine
View article: Die Nicht-Turing-Maschine: Grundzüge eines neuen maschinellen Ordnungstyps
Die Nicht-Turing-Maschine: Grundzüge eines neuen maschinellen Ordnungstyps Open
Diese Arbeit führt einen neuartigen Maschinentyp ein, der nicht auf Berechnung, Symbolverarbeitung oder probabilistischen Optimierungen basiert. Die Nicht-Turing-Maschine wird als strukturelle Ordnungseinheit beschrieben, deren Identität a…
View article: Die Nicht-Turing-Maschine: Grundzüge eines neuen maschinellen Ordnungstyps
Die Nicht-Turing-Maschine: Grundzüge eines neuen maschinellen Ordnungstyps Open
Diese Arbeit führt einen neuartigen Maschinentyp ein, der nicht auf Berechnung, Symbolverarbeitung oder probabilistischen Optimierungen basiert. Die Nicht-Turing-Maschine wird als strukturelle Ordnungseinheit beschrieben, deren Identität a…
View article: 图灵机空间的概率测度构造与复杂度函数Hilbert空间 A Probability Measure on Turing Machine Space and the Hilbert Space of Complexity Functions
图灵机空间的概率测度构造与复杂度函数Hilbert空间 A Probability Measure on Turing Machine Space and the Hilbert Space of Complexity Functions Open
本文在图灵机空间上构造自然的概率测度,并为复杂度函数建立严格的Hilbert空间理论框架
View article: 图灵机空间的概率测度构造与复杂度函数Hilbert空间 A Probability Measure on Turing Machine Space and the Hilbert Space of Complexity Functions
图灵机空间的概率测度构造与复杂度函数Hilbert空间 A Probability Measure on Turing Machine Space and the Hilbert Space of Complexity Functions Open
本文在图灵机空间上构造自然的概率测度,并为复杂度函数建立严格的Hilbert空间理论框架
View article: The Algorithmic Boundary of Group Isomorphism
The Algorithmic Boundary of Group Isomorphism Open
The Group Isomorphism Problem (GIP) asks whether two given finite groups are isomorphic. This fundamental question lies at a critical juncture of computational algebra and theoretical computer science, representing one of the most signific…
View article: The 3D Computational Architecture of Carbon–Base–Codon–Protein and the Emergence of a Natural Biological Computer
The 3D Computational Architecture of Carbon–Base–Codon–Protein and the Emergence of a Natural Biological Computer Open
This monograph presents the Energy Transmission Theory (ETT), a novel, independently developed scientific framework that fundamentally reinterprets life as an optimal 3D computational system governed by physical principles of energy flow, …
View article: The 3D Computational Architecture of Carbon–Base–Codon–Protein and the Emergence of a Natural Biological Computer
The 3D Computational Architecture of Carbon–Base–Codon–Protein and the Emergence of a Natural Biological Computer Open
This monograph presents the Energy Transmission Theory (ETT), a novel, independently developed scientific framework that fundamentally reinterprets life as an optimal 3D computational system governed by physical principles of energy flow, …
View article: General Computation using Slidable Tiles with Deterministic Global Forces
General Computation using Slidable Tiles with Deterministic Global Forces Open
We study the computational power of the Full-Tilt model of motion planning, where slidable polyominos are moved maximally around a board by way of a sequence of directional ``tilts.'' We focus on the deterministic scenario in which the til…
View article: The Algorithmic Boundary of Group Isomorphism
The Algorithmic Boundary of Group Isomorphism Open
The Group Isomorphism Problem (GIP) asks whether two given finite groups are isomorphic. This fundamental question lies at a critical juncture of computational algebra and theoretical computer science, representing one of the most signific…
View article: General Computation using Slidable Tiles with Deterministic Global Forces
General Computation using Slidable Tiles with Deterministic Global Forces Open
We study the computational power of the Full-Tilt model of motion planning, where slidable polyominos are moved maximally around a board by way of a sequence of directional ``tilts.'' We focus on the deterministic scenario in which the til…
View article: Manifesto: Why Systemic Coherence Supersedes Mathematical Reductionism – An Ontology for the Unified Universe
Manifesto: Why Systemic Coherence Supersedes Mathematical Reductionism – An Ontology for the Unified Universe Open
This document serves as the Epistemological Manifesto for the Systemic Universe (DSU) framework. It challenges the current paradigm of modern physics, which relies on the unproven assumption that reality is defined solely by mathematical q…
View article: Restoring TM Competency & Reputation: The Case Against Intractability through Modular Turing Machines
Restoring TM Competency & Reputation: The Case Against Intractability through Modular Turing Machines Open
This paper proposes a computational model, the Modular Turing Machine (MTM), developed under the philosophy of Fluid Computation, [1], to demonstrate that the classification of problems as NP-Complete is a flawed measure of the Turing Mach…
View article: Transformers as Universal Computation Engines: Theory and Empirical Validation
Transformers as Universal Computation Engines: Theory and Empirical Validation Open
This paper explores the theoretical capabilities and empirical performance of Transformer networks as universal computation engines. We delve into the Transformer architecture's ability to approximate any continuous function, analyzing its…
View article: The Measure-Theoretic Foundations of Algorithmic Randomness
The Measure-Theoretic Foundations of Algorithmic Randomness Open
This paper delves into the intricate relationship between measure theory and algorithmic randomness, establishing a rigorous framework for understanding what constitutes a truly random sequence. We explore how measure-theoretic concepts, p…
View article: The Measure-Theoretic Foundations of Algorithmic Randomness
The Measure-Theoretic Foundations of Algorithmic Randomness Open
This paper delves into the intricate relationship between measure theory and algorithmic randomness, establishing a rigorous framework for understanding what constitutes a truly random sequence. We explore how measure-theoretic concepts, p…
View article: Transformers as Universal Computation Engines: Theory and Empirical Validation
Transformers as Universal Computation Engines: Theory and Empirical Validation Open
This paper explores the theoretical capabilities and empirical performance of Transformer networks as universal computation engines. We delve into the Transformer architecture's ability to approximate any continuous function, analyzing its…
View article: Manifesto: Why Systemic Coherence Supersedes Mathematical Reductionism – An Ontology for the Unified Universe
Manifesto: Why Systemic Coherence Supersedes Mathematical Reductionism – An Ontology for the Unified Universe Open
This document serves as the Epistemological Manifesto for the Systemic Universe (DSU) framework. It challenges the current paradigm of modern physics, which relies on the unproven assumption that reality is defined solely by mathematical q…
View article: Restoring TM Competency & Reputation: The Case Against Intractability through Modular Turing Machines
Restoring TM Competency & Reputation: The Case Against Intractability through Modular Turing Machines Open
This paper proposes a computational model, the Modular Turing Machine (MTM), developed under the philosophy of Fluid Computation, [1], to demonstrate that the classification of problems as NP-Complete is a flawed measure of the Turing Mach…
View article: TuringLang/Turing.jl: v0.42.0
TuringLang/Turing.jl: v0.42.0 Open
Turing v0.42.0 Diff since v0.41.4 DynamicPPL 0.39 Turing.jl v0.42 brings with it all the underlying changes in DynamicPPL 0.39. Please see the DynamicPPL changelog for full details; in here we summarise only the changes that are most perti…
View article: The Architecture of Implicit Knowledge: Computational Models of Intuition from Quantum Probability to High-Dimensional Manifolds
The Architecture of Implicit Knowledge: Computational Models of Intuition from Quantum Probability to High-Dimensional Manifolds Open
This work develops a unified computational theory of intuition, reframing intuitive judgment as a mathematically tractable class of information-processing strategies rather than a mystical or heuristic residue. Integrating predictive proce…
View article: The Architecture of Implicit Knowledge: Computational Models of Intuition from Quantum Probability to High-Dimensional Manifolds
The Architecture of Implicit Knowledge: Computational Models of Intuition from Quantum Probability to High-Dimensional Manifolds Open
This work develops a unified computational theory of intuition, reframing intuitive judgment as a mathematically tractable class of information-processing strategies rather than a mystical or heuristic residue. Integrating predictive proce…
View article: Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal Spacetime
Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal Spacetime Open
Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal Spacetime The P versus NP problem has traditionally been viewed through the lens of pure mathematics and algorithmic complexity. Ho…
View article: Graph-Based Deterministic Polynomial Algorithm for NP Problems
Graph-Based Deterministic Polynomial Algorithm for NP Problems Open
The P vs NP problem asks whether every problem whose solution can be verified in polynomialtime (NP) can also be solved in polynomial time (P). In this paper, we present a proof that P =NP, demonstrating that every NP problem can be solved…
View article: Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal Spacetime
Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal Spacetime Open
Topological Renormalization of Information: Resolving P versus NP via Holographic Field Dynamics in Fractal Spacetime The P versus NP problem has traditionally been viewed through the lens of pure mathematics and algorithmic complexity. Ho…
View article: Graph-Based Deterministic Polynomial Algorithm for NP Problems
Graph-Based Deterministic Polynomial Algorithm for NP Problems Open
The P vs NP problem asks whether every problem whose solution can be verified in polynomialtime (NP) can also be solved in polynomial time (P). In this paper, we present a proof that P =NP, demonstrating that every NP problem can be solved…
View article: Bonded Science: Alan Turing Correction: Field-Based Computation Beyond the Limits of Turing Systems
Bonded Science: Alan Turing Correction: Field-Based Computation Beyond the Limits of Turing Systems Open
View article: Bonded Science: Alan Turing Correction: Field-Based Computation Beyond the Limits of Turing Systems
Bonded Science: Alan Turing Correction: Field-Based Computation Beyond the Limits of Turing Systems Open
View article: Information-Time of Quantum Observers: Geometry, Quantum Speed Limits, and Implications for Quantum Computing and AI
Information-Time of Quantum Observers: Geometry, Quantum Speed Limits, and Implications for Quantum Computing and AI Open
This paper introduces a notion of information-time for quantum observers, defined as the Bures length of the trajectory of an observer’s reduced density matrix in state space. In contrast to approaches where time is an external parameter o…
View article: Fractal Series — Paper 11: — Conclusion: Stability(x) and the Geometry of Meaning
Fractal Series — Paper 11: — Conclusion: Stability(x) and the Geometry of Meaning Open
TitleFractal Series — Conclusion: Stability(x) and the Geometry of Meaning AuthorJuan F. Culajay TypePreprint / Report LanguageEnglish LicenseSuggested: Creative Commons Attribution 4.0 International (CC BY 4.0) Abstract (Description) The …
View article: Super–Computable Numbers: A Structural Reinterpretation of Turing Computability via Super–Boolean Logic
Super–Computable Numbers: A Structural Reinterpretation of Turing Computability via Super–Boolean Logic Open
# Super–Computable Numbers ### A Structural Reinterpretation of Turing’s 1936 Computability Framework This record releases **version v1.0** of *Super–Computable Numbers*, a modernreinterpretation of Turing’s 1936 paper *“On Computable Numb…