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- Kohtaro Tadaki
- ArXiv
- 2002

We generalize the concept of randomness in an infinite binary sequence in order to characterize the degree of randomness by a real number D > 0. Chaitin’s halting probability Ω is generalized to ΩD whose degree of randomness is precisely D. On the basis of this generalization, we consider the degree of randomness of each point in Euclidean space through its… (More)

- Kohtaro Tadaki, Tomoyuki Yamakami, Jack C. H. Lin
- SOFSEM
- 2004

A theory of one-tape (one-head) linear-time Turing machines is essentially different from its polynomial-time counterpart since these machines are closely related to finite state automata. This paper discusses structural-complexity issues of one-tape Turing machines of various types (deterministic, nondeterministic, reversible, alternating, probabilistic,… (More)

- Shigeo Tsujii, Masahito Gotaishi, Kohtaro Tadaki, Ryou Fujita
- PQCrypto
- 2010

A New digital signature scheme based on Stepwise Triangular Scheme (STS) is proposed. The proposed trapdoor has resolved the vulnerability of STS and secure against both Gröbner Bases and Rank Attacks. In addition, as a basic trapdoor, it is more efficient than the existing systems. With the efficient implementation, the Multivariate Public Key… (More)

- Kohtaro Tadaki
- ArXiv
- 2010

In 1975 Chaitin introduced his Ω number as a concrete example of random real. The real Ω is defined based on the set of all halting inputs for an optimal prefix-free machine U , which is a universal decoding algorithm used to define the notion of program-size complexity. Chaitin showed Ω to be random by discovering the property that the first n bits of the… (More)

- Shigeo Tsujii, Kohtaro Tadaki, Ryou Fujita
- IACR Cryptology ePrint Archive
- 2004

- Kohtaro Tadaki
- ArXiv
- 2008

We develop a statistical mechanical interpretation of algorithmic information theory by introducing the notion of thermodynamic quantities, such as free energy, energy, statistical mechanical entropy, and specific heat, into algorithmic information theory. We investigate the properties of these quantities by means of program-size complexity from the point… (More)

- Kohtaro Tadaki
- 2009

Chaitin [G. J. Chaitin, J. Assoc. Comput. Mach., vol. 22, pp. 329–340, 1975] introduced Ω number as a concrete example of random real. The real Ω is defined as the probability that an optimal computer halts, where the optimal computer is a universal decoding algorithm used to define the notion of program-size complexity. Chaitin showed Ω to be random by… (More)

- Shigeo Tsujii, Kohtaro Tadaki, Ryou Fujita, Masahito Gotaishi, Toshinobu Kaneko
- IEICE Transactions
- 2009

Following the last proposal of the nonlinear Piece in Hand method, which has 3-layer structure, 2-layer nonlinear Piece in Hand method is proposed. Both of them aim at enhancing the security of existing and future multivariate public key cryptosystems. The new nonlinear Piece in Hand is compared with the 3-layer method and PMI+, which was proposed by Ding,… (More)

- Kohtaro Tadaki
- Math. Log. Q.
- 2006

This paper proposes an extension of Chaitin’s halting probability Ω to a measurement operator in an infinite dimensional quantum system. Chaitin’s Ω is defined as the probability that the universal self-delimiting Turing machine U halts, and plays a central role in the development of algorithmic information theory. In the theory, there are two equivalent… (More)

- Sandra Marder, T. Winkler, Kohtaro Tadaki, S R Bobbink, William O. Robertson
- Veterinary and human toxicology
- 2001

The State of Washington mandated the use of imprints on all prescription drugs in 1980 and for "OTC's" in 1991. The FDA implemented federal requirements in 1995. Unfortunately, the FDA permitted the continued use of symbols, logotypes, and trademarks as code components, limiting the use of automated recognition systems. Analyses of several week-long samples… (More)