On Asymptotic Probabilities of Monadic Second Order
نویسنده
چکیده
We propose a new, general and easy method for proving nonexistence of asymptotic probabilities of monadic second{order sentences in classes of nite structures where rst{order extension axioms hold almost surely.
منابع مشابه
Nonconvergence, undecidability, and intractability in asymptotic problems
Results delimiting the logical and effective content of asymptotic combinatorics are presented. For the class of binary relations with an underlying linear order, and the class of binary functions, there are properties, given by first-order sentences, without asymptotic probabilities; every first-order asymptotic problem (i.e., set of first-order sentences with asymptotic probabilities bounded ...
متن کاملA logical approach to asymptotic combinatorics II: Monadic second-order properties
In Compton [3] we began an investigation of a general approach to asymptotic problems in combinatorics. These problems involve determining probabilities of certain properties holding in large, finite structures randomly chosen from certain classes. The properties we considered were those expressible in first order logic L,,, and the classes were those closed under disjoint unions and components...
متن کاملMonadic Second Order Probabilities in Algebra
We analyze the question of existence of asymptotic cumulative probabilities for monadic second order deenable properties of nite algebras. We focus our attention on the directly representable varieties and on the variety of groups. We prove in a very strong way that some recently proven rst-order 0{1 laws and limit laws for these varieties cannot be extended to monadic second order logic. Namel...
متن کاملMonadic Second Order Asymptotics on Random Acyclic Graphs
We classify the vertices of trees, and use a primitive Poisson approximation argument to prove that almost all trees have almost the same proportion of vertices of each kind. We use a graph surgery construction to investigate the asymptotic probabilities of order-invariant Monadic Second Order (with built-in linear ordering) queries over random free trees, proving that for any MSO query , the p...
متن کاملConvergence laws for random words
A random word is a finite sequence of symbols chosen independently at random from some finite alphabet. The probability distribution of the symbols may be constant, or it may depend on the length of the word, analogo'Us to the way that edge probabilities of a random graph depend on the number of vertices of the graph. Two formal languages which express properties of words are considered: a firs...
متن کامل