Computational Principle Boundary Theory (CPBT) is a framework that formalises the relationship between a system's computational principles and its inherent capability limits. By representing computational power as a function of underlying principles and constraints, CPBT provides a unified method for analysing the theoretical upper bounds of any computational model. This paper introduces the core concepts of CPBT, develops a mathematical representation of the principle-ability boundary, explores its implications for classical and quantum models, and demonstrates how CPBT can guide the design of future computational architectures. The theory is expressed entirely in plain text, with all mathematical notation rendered in standard ASCII format to facilitate easy copying and pasting. The discussion is limited to theoretical analysis, and no experimental data or tables are presented.
Computational Principle Boundary Theory (CPBT) is a framework that formalises the relationship between a system's computational principles and its inherent capability limits. By representing computational power as a function of underlying principles and constraints, CPBT provides a unified method for analysing the theoretical upper bounds of any computational model. This paper introduces the core concepts of CPBT, develops a mathematical representation of the principle-ability boundary, explores its implications for classical and quantum models, and demonstrates how CPBT can guide the design of future computational architectures. The theory is expressed entirely in plain text, with all mathematical notation rendered in standard ASCII format to facilitate easy copying and pasting. The discussion is limited to theoretical analysis, and no experimental data or tables are presented.
Computational Boundary Transfer Theory, abbreviated CBTT, proposes a principled framework for translating constraints and capabilities that are traditionally defined in one computational paradigm into an equivalent formulation in another paradigm. The central insight is that many seemingly unrelated computational limits, such as time and space bounds for Turing machines, depth and width constraints for neural networks, and communication complexity for distributed systems, can be mapped onto a common boundary space. By constructing explicit mapping functions between these boundary spaces, CBTT enables the transfer of results, intuitions, and techniques across domains that have historically been studied in isolation. This paper develops the formal underpinnings of CBTT, introduces a generic boundary mapping function f that transforms a computational boundary expressed in one model into its counterpart in another model, and demonstrates how the theory unifies several prominent computational limit frameworks. We illustrate the theory through several canonical examples, including the transfer from classical decision tree depth limits to modern deep learning architecture depth limits, and from quantum circuit depth limits to classical circuit depth limits. The theory also provides a potential pathway to a more general understanding of the computational power of hybrid models, such as quantum neural networks. CBTT's ability to bridge discrete and continuous computational boundaries suggests that the theory could serve as a foundational tool for future research in complexity theory, algorithm design, and artificial intelligence. The paper concludes with a discussion of potential implications for the Turing Award and outlines directions for future investigations that could expand the reach of CBTT to emerging computational paradigms.
This paper introduces the concept of Computational Substrate Independence, a theoretical framework designed to address the fundamental question of whether equivalent computational capabilities remain the same regardless of the underlying physical or software substrate. The core challenge lies in defining a rigorous criterion for determining when a computation, expressed in one form, can be faithfully replicated across radically different computational environments – encompassing classical computers, quantum computers, neuromorphic systems, and potentially entirely novel computational media. The paper lays out the key principles of this theory, focusing on the preservation of algorithmic information and the transformation rules necessary to achieve substrate independence. It explores the implications of this concept for various emerging computing paradigms and proposes a formalization of the necessary conditions for substrate-independent computation. The central argument posits that the essence of computation resides not in the specific implementation, but in the logical structure and information flow represented by the algorithm.
Computational Representation Universe Theory (CRUT) proposes a unified framework that treats the entire observable universe as a computational structure generated by a set of fundamental representation rules. The theory is built on the premise that every conceivable physical state can be expressed as an element of a high‑dimensional representation space denoted by Ω_R. By formalizing the mapping from physical observables to elements of Ω_R and defining a set of transformation operators that emulate physical interactions, CRUT offers a deterministic yet flexible computational model that reconciles quantum superposition, classical determinism, and relativistic constraints within a single mathematical formalism. This paper details the core assumptions of CRUT, develops its mathematical foundation, demonstrates its computational implementation, and discusses its potential implications for physics, information theory, and the philosophy of science.
This paper proposes a novel computational architecture predicated on the utilization of quantum frontiers – specifically, quantum superposition and entanglement – as the fundamental computational units. Traditional quantum computing approaches often rely on manipulating qubits in specific, well-defined states, limiting their potential for complex calculations. This architecture, termed "Quantum Frontiers," shifts the paradigm by embracing the inherent complexity and interconnectedness of quantum states at their most basic level. We detail a framework for designing algorithms and hardware that directly leverage superposition and entanglement, aiming to unlock computational capabilities beyond the constraints of current methodologies. The core concept involves treating the dynamic evolution of quantum states – the inherent "frontier" – as the primary computational process. This approach offers a potential pathway to overcome limitations associated with qubit control fidelity and algorithm design in conventional quantum computing. The proposed architecture utilizes a layered design, incorporating a quantum state preparation layer, a dynamic quantum processing layer, and a measurement/output layer. Mathematical formulations are presented to illustrate key concepts and operational principles. The architecture's adaptability and potential impact on future quantum computation are discussed.
The rapid diversification of computational paradigms—from classical sequential logic, through parallel and distributed architectures, to quantum, neuromorphic, and probabilistic models—has produced a fragmented landscape of theoretical frameworks, each with its own primitives, constraints, and application domains. The Computational Paradigm Fusion Theory (CPFT) proposes a unifying formalism that systematically combines distinct paradigms into higher‑level hybrid models. At its core, CPFT introduces a compositional operation, denoted by '+', that takes two paradigms, Paradigm_A and Paradigm_B, and yields a fused paradigm, Paradigm_C. This operation is defined through a set of compatibility rules, resource sharing constraints, and cross‑paradigm communication primitives. The theory provides explicit construction guidelines for the state space, transition functions, and observable outputs of the fused system, ensuring that the resulting model preserves the computational power of its constituents while enabling new algorithmic possibilities. By demonstrating that CPFT subsumes existing hybrid models such as MapReduce, quantum‑classical co‑processing, and spiking neural‑network‑augmented Turing machines, we argue that CPFT constitutes a foundational framework for the next generation of computational theory. The potential for CPFT to reshape the theoretical underpinnings of computing and to inspire novel algorithmic breakthroughs positions it as a strong candidate for recognition at the highest levels of computational research, including the Turing Award.
Quantum computing overcomes the limitations of computational power in classical computing by utilizing the principles of quantum mechanics; it has a transformative impact on improving computational effectiveness in data analysis. The existing industrial sectors are unclear how to apply theories and concepts into applications of quantum computing though there are many research studies. Therefore, this study aims to review the current state-of-the-art of quantum computing algorithms by discussing their mathematical frameworks, underlying architectures, and applications, and propose a novel ontology-based quantum architecture model for developers to select, filter and cascade different components for implementation. A case study is used to demonstrate the effectiveness of using the proposed model to design and implementation of a quantum computing algorithm with the proposed model. The results found the ontology model is easy to understand, ease of use, with available resources and technology facilitating for guiding developer on the development of a quantum application starting from problem definition to human problem-solving processes, and a quantum computing design.