1,566 research outputs found

    Equilibrium Points of an AND-OR Tree: under Constraints on Probability

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    We study a probability distribution d on the truth assignments to a uniform binary AND-OR tree. Liu and Tanaka [2007, Inform. Process. Lett.] showed the following: If d achieves the equilibrium among independent distributions (ID) then d is an independent identical distribution (IID). We show a stronger form of the above result. Given a real number r such that 0 < r < 1, we consider a constraint that the probability of the root node having the value 0 is r. Our main result is the following: When we restrict ourselves to IDs satisfying this constraint, the above result of Liu and Tanaka still holds. The proof employs clever tricks of induction. In particular, we show two fundamental relationships between expected cost and probability in an IID on an OR-AND tree: (1) The ratio of the cost to the probability (of the root having the value 0) is a decreasing function of the probability x of the leaf. (2) The ratio of derivative of the cost to the derivative of the probability is a decreasing function of x, too.Comment: 13 pages, 3 figure

    Resource Bounded Immunity and Simplicity

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    Revisiting the thirty years-old notions of resource-bounded immunity and simplicity, we investigate the structural characteristics of various immunity notions: strong immunity, almost immunity, and hyperimmunity as well as their corresponding simplicity notions. We also study limited immunity and simplicity, called k-immunity and feasible k-immunity, and their simplicity notions. Finally, we propose the k-immune hypothesis as a working hypothesis that guarantees the existence of simple sets in NP.Comment: This is a complete version of the conference paper that appeared in the Proceedings of the 3rd IFIP International Conference on Theoretical Computer Science, Kluwer Academic Publishers, pp.81-95, Toulouse, France, August 23-26, 200

    Role of the Landau-Migdal Parameters with the Pseudovector and the Tensor Coupling in Relativistic Nuclear Models -- The Quenching of the Gamow-Teller Strength --

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    Role of the Landau-Migdal parameters with the pseudovector (gag_a) and the tensor coupling (gtg_t) is examined for the giant Gamow-Teller (GT) states in the relativistic random phase approximation (RPA). The excitation energy is dominated by both gag_a and gtg_t in a similar way, while the GT strength is independent of gag_a and gtg_t in the RPA of the nucleon space, and is quenched, compared with that in non-relativistic one. The coupling of the particle-hole states with nucleon-antinucleon states is expected to quench the GT strength further through gag_a.Comment: 7 pages, ReVTe