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SO(...) Sentences and Their Asymptotic Probabilities
"... We prove a 01 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 01 laws for fragments of second order logic (with equality) defined in ..."
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We prove a 01 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 01 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 01 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 01 laws for fragments of \Sigma 1 1 defined in terms of first order quantifier prefixes (see [3, 4, 5]). The class...
Infinitary Queries and Their Asymptotic Probabilities I:
"... Properties Definable in Transitive Closure Logic appeared in: E. B"orger et al. eds., Proc. CSL'91, Springer Lecture Notes in ..."
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Properties Definable in Transitive Closure Logic appeared in: E. B"orger et al. eds., Proc. CSL'91, Springer Lecture Notes in
On Asymptotic Probabilities of Monadic Second Order Properties
"... We propose a new, general and easy method for proving nonexistence of asymptotic probabilities of monadic secondorder sentences in classes of finite structures where firstorder extension axioms hold almost surely. ..."
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We propose a new, general and easy method for proving nonexistence of asymptotic probabilities of monadic secondorder sentences in classes of finite structures where firstorder extension axioms hold almost surely.
Asymptotic Probability Density Function of Nonlinear Phase Noise
, 2003
"... The asymptotic probability density function of nonlinear phase noise, often called the GordonMollenauer 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 chisquare random ..."
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The asymptotic probability density function of nonlinear phase noise, often called the GordonMollenauer 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 chisquare random
Critical Power for Asymptotic Connectivity in Wireless Networks
, 1998
"... : In wireless data networks each transmitter's power needs to be high enough to reach the intended receivers, while generating minimum interference on other receivers sharing the same channel. In particular, if the nodes in the network are assumed to cooperate in routing each others ' pack ..."
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Cited by 541 (19 self)
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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
Asymptotic probability extraction for nonnormal performance distributions
 IEEE TRANS. CAD
, 2007
"... While process variations are becoming more significant with each new IC technology generation, they are often modeled via linear regression models so that the resulting performance variations can be captured via normal distributions. Nonlinear response surface models (e.g., quadratic polynomials) c ..."
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Cited by 20 (10 self)
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distribution by an efficient rational function. It is proven that such a momentmatching 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
Asymptotic probabilities of extension properties and random lcolourable structures
 Annals of Pure and Applied Logic
"... ar ..."
Asymptotic Probability Extraction for NonNormal Distributions of Circuit Performance
 IEEE ICCAD
, 2004
"... While process variations are becoming more significant with each new IC technology generation, they are often modeled via linear regression models so that the resulting performance variations can be captured via Normal distributions. Nonlinear (e.g. quadratic) response surface models can be utilized ..."
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Cited by 51 (7 self)
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be utilized to capture larger scale process variations; however, such models result in nonNormal 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
Singular Combinatorics
 ICM 2002 VOL. III 13
, 2002
"... 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. " ..."
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Cited by 800 (10 self)
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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
On Asymptotic Probabilities in Logics That Capture DSPACE(log n) in Presence of Ordering?
"... Abstract. We show that for logics that capture DSPACE(log n) over ordered structures, and for recursive probability distributions on the class of finite models of the signature, the 01 law and the convergence law hold if and only if certain boundedness conditions are satisfied. As one of the applic ..."
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of the applications, we consider the conjecture of Kolaitis and Vardi, stating that for arbitrary probability distributions the 01 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
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