Katherine St. John. Limit probabilities for random sparse bit strings. Electronic Journal of Combinatorics, 4(1):R23, 1997. This article was processed using the L A T E X macro package with LLNCS style  Home/Search   Document Details and Download   Summary   Related Articles

....Dolan [2] showed that for p(n) n Gamma1 and n Gamma1 p(n) n Gamma1=2 for every OE, a OE = 0 or 1 in Equation 1. This stronger convergence is called a Zero One Law for U n;p . Dolan also showed that the Zero One Law does not hold for n Gamma1=k p(n) n Gamma1= k 1) k 1. In [14], we examine the random sparse bit strings with probability p(n) c=n and give a finer analysis than convergence. For this choice of p, we have the limit probabilities of OE are either i=m X i=1 e Gammac c t i t i or 1 Gamma i=m X i=1 e Gammac c t i t i for some (possibly ....

....a, S [ oe a;t j= OE. So, f OE (c) is constantly 1, and OE 2 S c for every c. Therefore, S = T c S c . a 5 Future Work The work of [11] and [12] characterize the almost sure theories and their countable models for p(n) n Gamma1 and n Gamma1=k p(n) n Gamma1= k 1) for k 1. In [14] and this paper, we fill the gaps between these theories by characterizing the almost sure theories of U n; c n and U n; c p n and giving the form of the function f OE (c) for each first order sentence OE. Monadic second order logic is more expressive than first order logic over bit ....

Katherine St. John. Limit probabilities for random sparse bit strings. Electronic Journal of Combinatorics, 4(1):R23, 1997. This article was processed using the L A T E X macro package with LLNCS style

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