Related papers: MSO 0-1 law for recursive random trees
We introduce the branching transitive closure operator on weighted monadic second-order logic formulas where the branching corresponds in a natural way to the branching inherent in trees. For arbitrary commutative semirings, we prove that…
We study tree-to-tree transformations that can be defined in first-order logic or monadic second-order logic. We prove a decomposition theorem, which shows that every transformation can be obtained from prime transformations, such as…
We construct a two-dimensional counterexample of a random walk in random environment (RWRE). The environment is stationary, mixing and perturbative, and the corresponding RWRE has non-trivial probability to wander off to the upper right.…
We give a new simple proof of the decidability of the First Order Theory of (omega^omega^i,+) and the Monadic Second Order Theory of (omega^i,<), improving the complexity in both cases. Our algorithm is based on tree automata and a new…
Weighted recursive trees are built by adding successively vertices with predetermined weights to a tree: each new vertex is attached to a parent chosen randomly proportionally to its weight. Under some assumptions on the sequence of…
One of Courcelle's celebrated results states that if C is a class of graphs of bounded tree-width, then model-checking for monadic second order logic is fixed-parameter tractable on C by linear time parameterised algorithms. An immediate…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
Uniform attachment with freezing is an extension of the classical model of random recursive trees, in which trees are recursively built by attaching new vertices to old ones. In the model of uniform attachment with freezing, vertices are…
We consider root-finding algorithms for random rooted trees grown by uniform attachment. Given an unlabeled copy of the tree and a target accuracy $\varepsilon > 0$, such an algorithm outputs a set of nodes that contains the root with…
We study the problem of learning properties of nodes in tree structures. Those properties are specified by logical formulas, such as formulas from first-order or monadic second-order logic. We think of the tree as a database encoding a…
Let $\alpha \in (0,1)_{\mathbb{R}}$ be irrational and $G_n = G_{n,1/n^\alpha}$ be the random graph with edge probability $1/n^\alpha$; we know that it satisfies the 0-1 law for first order logic. We deal with the failure of the 0-1 law for…
The finite satisfiability problem of monadic second order logic is decidable only on classes of structures of bounded tree-width by the classic result of Seese (1991). We prove the following problem is decidable: Input: (i) A monadic second…
Permutations can be viewed as pairs of linear orders, or more formally as models over a signature consisting of two binary relation symbols. This approach was adopted by Albert, Bouvel and F\'eray, who studied the expressibility of…
We deal with the monadic (second-order) theory of order. We prove all known results in a unified way, show a general way of reduction, prove more results and show the limitation on extending them. We prove (CH) that the monadic theory of…
We show a theorem on monadic second-order k-ary queries on finite words. It may be illustrated by the following example: if the number of results of a query on binary strings is O(number of 0s $\times$ number of 1s), then each result can be…
We study the model-checking problem for recursion schemes: does the tree generated by a given higher-order recursion scheme satisfy a given logical sentence. The problem is known to be decidable for sentences of the MSO logic. We prove…
We study the first-order model checking problem on two generalisations of pushdown graphs. The first class is the class of nested pushdown trees. The other is the class of collapsible pushdown graphs. Our main results are the following.…
We examine a discrete random recursive tree growth process that, at each time step, either adds or deletes a node from the tree with probability $p$ and $1-p$, respectively. Node addition follows the usual uniform attachment model. For node…
Order-invariant formulas access an ordering on a structure's universe, but the model relation is independent of the used ordering. Order invariance is frequently used for logic-based approaches in computer science. Order-invariant formulas…
We prove that the size of the largest common subtree between two uniform, independent, leaf-labelled random binary trees of size $n$ is typically less than $n^{1/2-\varepsilon}$ for some $\varepsilon>0$. Our proof relies on the coupling…