Towards Combining Dense Linear Order with Random Graph
نویسندگان
چکیده
In this paper we present our work in progress towards obtaining a Nelson-Oppen style combination for combining quantified theories, where each individual component theory admits quantifier elimination. We introduces the notion of good model for union theories, for which there exists a simple quantifier elimination scheme that uses the elimination procedures for individual component theories as black boxes. We show that a good model exists for the union theory of dense linear order and random graph, and it coincides with the Fraı̈ssé limit of the class of finite graph with ordered vertices.
منابع مشابه
How many random edges make a dense graph hamiltonian?
This paper investigates the number of random edges required to add to an arbitrary dense graph in order to make the resulting graph hamiltonian with high probability. Adding (n) random edges is both necessary and sufficient to ensure this for all such dense graphs. If, however, the original graph contains no large independent set, then many fewer random edges are required. We prove a similar re...
متن کاملTowards Resistance Sparsifiers
We study resistance sparsification of graphs, in which the goal is to find a sparse subgraph (with reweighted edges) that approximately preserves the effective resistances between every pair of nodes. We show that every dense regular expander admits a (1 + ε)-resistance sparsifier of size Õ(n/ε), and conjecture this bound holds for all graphs on n nodes. In comparison, spectral sparsification i...
متن کاملDense image registration through MRFs and efficient linear programming
In this paper, we introduce a novel and efficient approach to dense image registration, which does not require a derivative of the employed cost function. In such a context, the registration problem is formulated using a discrete Markov random field objective function. First, towards dimensionality reduction on the variables we assume that the dense deformation field can be expressed using a sm...
متن کاملThe Average Distance in a Random Graph with Given Expected Degrees
Random graph theory is used to examine the “smallworld phenomenon” – any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n/ log d̃ where d̃ is the weighted average of the sum of squares of the expected degrees. Of particular interest ar...
متن کاملOn the commuting graph of non-commutative rings of order $p^nq$
Let $R$ be a non-commutative ring with unity. The commuting graph of $R$ denoted by $Gamma(R)$, is a graph with vertex set $RZ(R)$ and two vertices $a$ and $b$ are adjacent iff $ab=ba$. In this paper, we consider the commuting graph of non-commutative rings of order pq and $p^2q$ with Z(R) = 0 and non-commutative rings with unity of order $p^3q$. It is proved that $C_R(a)$ is a commutative ring...
متن کامل