By Frank Harary (auth.), C. S. Calude, M. J. Dinneen, S. Sburlan (eds.)
This quantity includes the papers offered on the 3rd Discrete arithmetic and Theoretical computing device technological know-how convention (DMTCS1), which used to be held at 'Ovidius'University Constantza, Romania in July 2001.
The convention was once open to all parts of discrete arithmetic and theoretical machine technological know-how, and the papers contained inside this quantity conceal issues akin to: summary info kinds and requirements; algorithms and knowledge constructions; automata and formal languages; computability, complexity and positive arithmetic; discrete arithmetic, combinatorial computing and type idea; good judgment, nonmonotonic good judgment and hybrid structures; molecular computing.
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Additional info for Combinatorics, Computability and Logic: Proceedings of the Third International Conference on Combinatorics, Computability and Logic, (DMTCS’01)
The minimum length of lO-chains for n is denoted by lO(n) . In 1937, Schloz  conjectured that, for all n l(2n - 1) $ n + l(n) - ~ 1, we have 1. Some times this conjecture is called the Scholz-Brauer conjecture . It is known that this conjecture is true for v( n) $ 4, where v( n) be the number of l's in the binary representation of n. Brauer  proved that it is true when l(n) = l*(n). Hansen  proved that the Scholz conjecture is true when l(n) = lO(n). Hebb  proved that the Scholz conjecture is true when l(n) = l**(n).
So, in order to prove the SB and AS conjectures for all positive integers we may need to solve this problem. 4 Conclusion We have given a generalization of star chain to M B-chain and conjectured that lO(n) = 1MB(n) and proved that it is true for integers n ~ 8 x 104 • Also, we have shown that the SB and AS conjectures and l(n) = lO(n) = 1MB(n) are true for integers n ~ 8 x 104 • References 1. W. Aiello and M. Subbarao: A conjecture in addition chains related to Scholz's conjecture. Comp. 6 (1993), 17-23.
1 (1936) 87-9l. Rouse Ball, W. W.  Mathematical Recreations and Essays, 1905. Royce, J.  The world and the individual, 1899. Russell, B.  The principles of mathematics, 1903. 31 Shashkin, Y.  Fixed Points, American Mathematical Society, 1991. Singh, P.  The socalled Fibonacci numbers in Ancient and Medieval India, Hist. Math. 12 (1985) 229-244. Skewes, S.  On the difference 1I'(x) -li(x), J. Math. Soc. 8 (1933) 277-283. Tarski, A. dia Phil. 1 (1936) 261-405.  A lattice-theoretical fixed-point theorem and its applications, Pac.