We prove a 0-1 law for the fragment of second order logic SO(89 ) over parametric classes of structures which allow only one unary atomic type, confirming partially a conjecture of Lacoste. This completes the investigation of 0-1 laws for fragments of second order logic (with equality) defined in terms of first order quantifier prefixes over, e.g., simple graphs and tournaments. We also prove a low oscillation law, and establish the 0-1 law for \Sigma 1 4 (89 ) without any restriction on the number of unary types. The research of this author was begun at the RWTH Aachen and finished at the University of Warsaw. He has been supported by Polish KBN grant 8 T11C 002 11 and by the German Science Foundation DFG. Both authors are grateful to Kevin Compton for a helpful discussion concerning this work. 1 Introduction Kolaitis and Vardi initiated the investigation of 0-1 laws for fragments of \Sigma 1 1 defined in terms of first order quantifier prefixes (see [3, 4, 5]). The class...

Properties Definable in Transitive Closure Logic appeared in: E. B"orger et al. eds., Proc. CSL'91, Springer Lecture Notes in

We propose a new, general and easy method for proving nonexistence of asymptotic probabilities of monadic second-order sentences in classes of finite structures where first-order extension axioms hold almost surely.

The asymptotic probability density function of nonlinear phase noise, often called the Gordon-Mollenauer effect, is derived analytically when the number of fiber spans is very large. The nonlinear phase noise is the summation of infinitely many independently distributed noncentral chi-square random

as the number of nodes in the network goes to infinity. It is shown that if n nodes are placed in a disc of unit area in ! 2 and each node transmits at a power level so as to cover an area of ßr 2 = (log n + c(n))=n, then the resulting network is asymptotically connected with probability one if and only

distribution by an efficient rational function. It is proven that such a moment-matching approach is asymptotically convergent when applied to quadratic response surface models. In addition, a number of novel algorithms and methods, including binomial moment evaluation, PDF/CDF shifting, nonlinear companding

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be utilized to capture larger scale process variations; however, such models result in non-Normal distributions for circuit performance which are difficult to capture since the distribution model is unknown. In this paper we propose an asymptotic probability extraction method, APEX, for estimating the unknown

Combinatorial enumeration leads to counting generating functions presenting a wide variety of analytic types. Properties of generating functions at singularities encode valuable information regarding asymptotic counting and limit probability distributions present in large random structures

of the applications, we consider the conjecture of Kolaitis and Vardi, stating that for arbitrary probability distributions the 0-1 law holds for the logic L!1! iff the same law holds for fixpoint logic. 1 Introduction 1.1 About the theory of asymptotic probabilities The problems considered in this paper belong