arXiv subjects

Tatsuaki Okamoto

Publications and source records attributed to Tatsuaki Okamoto.

4 recordsLinked to original sources

arXiv2026

On the Arrow of Time and Organized Complexity in the Universe

There is a widespread assumption that the universe in general, and the Earth's biosphere in particular, is becoming more complex over time. This paper formulates this assumption as a macroscopic law, the law of increasing complexity, for a system over a finite time span. It hypothesizes that this macroscopic law emerges in certain non-equilibrium systems with abundant free energy flows, such as the observable universe and the Earth's biosphere. We distinguish between two types of complexity: disorganized and organized. The complexity associated with this assumption is organized complexity. To formulate this law, we employ a quantitative definition of organized complexity as applied to probability distributions. We represent any object of complexity as the source of its observed value, which is expressed as a probability distribution; this enables a unified treatment of diverse objects. This formulation necessitates the use of observation systems to represent these objects. We introduce an order relation between these observation systems to demonstrate that the complexity of an object possesses a generic property, one that does not depend on any specific observation system. This paper develops a novel methodology for this macroscopic law, which formulates the arrow of time in terms of increasing organized complexity for certain non-equilibrium systems. This contrasts with the second law of thermodynamics, which formulates the arrow of time in terms of increasing disorganized complexity (entropy) for isolated systems. We apply this formulation to the fine-tuning problem: the puzzling observation that the fundamental physical constants appear to be fine-tuned for life on Earth. Our new explanation of the fine-tuning problem posits that these constants are fine-tuned for the emergence of the law of increasing complexity.

physics.hist-ph↗

arXiv2016

A Unified Paradigm of Organized Complexity and Semantic Information Theory

One of the most fundamental problems in science is to define {\it quantitatively} the complexity of organized matters, i.e., {\it organized complexity}. Although many measures have been proposed toward this aim in previous decades, there is no agreed upon definition. This paper presents a new quantitative definition of organized complexity. This definition {\it simultaneously} captures the three major features of complexity: computational (similar to logical depth), descriptional (similar to the Kolmogorov complexity and effective complexity) and distributional (similar to statistical complexity). In addition, the proposed definition is computable and can measure both probabilistic and deterministic forms of objects in a unified manner. The proposed definition is based on circuits rather than Turing machines and $ε$-machines. We give several criteria required for organized complexity measures and show that the proposed definition satisfies all of them for the first time. We then apply this quantitative definition to formulate a {\it semantic information theory}. We present the first formal definition of a {\it semantic information amount}, which is the core concept of the semantic information theory, that is based only on concretely defined notions. Previous semantic information theories defined this amount under some a priori information which is not concretely specified. We then unveil several fundamental properties in the semantic information theory, e.g., a semantic source coding theorem, semantic channel coding theorem, and effectiveness coding theorem. Although the semantic information theory has a long history of research going back more than six decades, there has been no study on its relation to organized complexity. This paper offers the first unified paradigm of organized complexity and semantic information theory.

cs.IT↗

arXiv2012

A Cryptographic Moving-Knife Cake-Cutting Protocol

This paper proposes a cake-cutting protocol using cryptography when the cake is a heterogeneous good that is represented by an interval on a real line. Although the Dubins-Spanier moving-knife protocol with one knife achieves simple fairness, all players must execute the protocol synchronously. Thus, the protocol cannot be executed on asynchronous networks such as the Internet. We show that the moving-knife protocol can be executed asynchronously by a discrete protocol using a secure auction protocol. The number of cuts is n-1 where n is the number of players, which is the minimum.

cs.GT↗

arXiv2005

Resource Bounded Unprovability of Computational Lower Bounds

This paper introduces new notions of asymptotic proofs, PT(polynomial-time)-extensions, PTM(polynomial-time Turing machine)-omega-consistency, etc. on formal theories of arithmetic including PA (Peano Arithmetic). This paper shows that P not= NP (more generally, any super-polynomial-time lower bound in PSPACE) is unprovable in a PTM-omega-consistent theory T, where T is a consistent PT-extension of PA. This result gives a unified view to the existing two major negative results on proving P not= NP, Natural Proofs and relativizable proofs, through the two manners of characterization of PTM-omega-consistency. We also show that the PTM-omega-consistency of T cannot be proven in any PTM-omega-consistent theory S, where S is a consistent PT-extension of T.

cs.CC↗