Kohtaro Tadaki

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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)
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)
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)
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)
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)
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)
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)