相关论文: From Philosophy to Program Size
There is a cognitive limit in Human Mind. This cognitive limit has played a decisive role in almost all fields including computer sciences. The cognitive limit replicated in computer sciences is responsible for inherent Computational…
This book presents a methodology and philosophy of empirical science based on large scale lossless data compression. In this view a theory is scientific if it can be used to build a data compression program, and it is valuable if it can…
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…
The classical view of epistemic logic is that an agent knows all the logical consequences of their knowledge base. This assumption of logical omniscience is often unrealistic and makes reasoning computationally intractable. One approach to…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
The aim of this paper is to undertake an experimental investigation of the trade-offs between program-size and time computational complexity. The investigation includes an exhaustive exploration and systematic study of the functions…
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative.…
This is a chapter in the Encyclopedia of Robotics. It is devoted to the study of complexity of complete (or exact) algorithms for robot motion planning. The term ``complete'' indicates that an approach is guaranteed to find the correct…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
A major part of computability theory focuses on the analysis of a few structures of central importance. As a tool, the method of coding with first-order formulas has been applied with great success. For instance, in the c.e. Turing degrees,…
Biology has taken strong steps towards becoming a computer science aiming at reprogramming nature after the realisation that nature herself has reprogrammed organisms by harnessing the power of natural selection and the digital prescriptive…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
Philosophical thinking has a side effect: by aiming to find the essence of a diverse set of phenomena, it often makes it difficult to see the differences between them. This can be the case with Mathematics, Programming, Writing and…
This is yet another version of the course notes in chao-dyn/9407003. Here we change the universal Turing machine that is used to measure program-size complexity so that the constants in our information-theoretic incompleteness theorems are…
In this paper, we present a theoretical effort to connect the theory of program size to psychology by implementing a concrete language of thought with Turing-computable Kolmogorov complexity (LT^2C^2) satisfying the following requirements:…
The paper elaborates an endeavor on applying the algorithmic information-theoretic computational complexity to meta-social-sciences. It is motivated by the effort on seeking the impact of the well-known incompleteness theorem to the…
In this paper we prove Chaitin's ``heuristic principle'', {\it the theorems of a finitely-specified theory cannot be significantly more complex than the theory itself}, for an appropriate measure of complexity. We show that the measure is…
A century ago, discoveries of a serious kind of logical error made separately by several leading mathematicians led to acceptance of a sharply enhanced standard for rigor within what ultimately became the foundation for Computer Science. By…
This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground…