Related papers: On finite width questionable representations of or…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
Compositions of tree-walking tree transducers form a hierarchy with respect to the number of transducers in the composition. As main technical result it is proved that any such composition can be realized as a linear bounded composition,…
Many data management applications must deal with data which is uncertain, incomplete, or noisy. However, on existing uncertain data representations, we cannot tractably perform the important query evaluation tasks of determining query…
We introduce a recursive method to deconstruct the automorphism group of an ordered set. By connecting this method with deep results for permutation groups, we prove the Automorphism Conjecture for ordered sets of width less than or equal…
We study the number of linear extensions of a partial order with a given proportion of comparable pairs of elements, and estimate the maximum and minimum possible numbers. We also consider a random interval partial order on $n$ elements,…
A linear ordering is called context-free if it is the lexicographic ordering of some context-free language and is called scattered if it has no dense subordering. Each scattered ordering has an associated ordinal, called its rank. It is…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…
We present a hereditary class of graphs of unbounded clique-width which is well-quasi-ordered by the induced subgraph relation. This result provides a negative answer to the question asked by Daligault, Rao and Thomass\'e in…
We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…
We introduce a reducibility on classes of structures, essentially a uniform enumeration reducibility. This reducibility is inspired by the Friedman-Stanley paper on using Borel reductions to compare classes of countable structures. This…
We analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set $P$ and are asked to identify a linear extension of $P$ using pairwise comparisons. For the standard sorting…
We consider a category of all finite partial orderings with quotient maps as arrows and construct a Fra\"iss\'e sequence in this category. Then we use commonly known relations between partial orders and lattices to construct a sequence of…
In this paper, we extend the notion of orthogonality to the general elements of an absolute matrix order unit space and relate it to the orthogonality among positive elements. We introduce the notion of a partial isometry in an absolute…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
The aim of this article is to show that systems of linear partial differential equations on filtered manifolds, which are of weighted finite type, can be canonically rewritten as first order systems of a certain type. This leads immediately…
We study the reverse mathematics of interval orders. We establish the logical strength of the implications between various definitions of the notion of interval order. We also consider the strength of different versions of the…
A sequence is called $C$-finite if it satisfies a linear recurrence with constant coefficients. We study sequences which satisfy a linear recurrence with $C$-finite coefficients. Recently, it was shown that such $C^2$-finite sequences…
A partially ordered set P is representable if there is a bounded distributive lattice such that its ordered set of prime ideals is order-isomorphic to P. We show that if the order components of a poset P are representable, then so is P.…
Using a recently introduced algebraic framework for the classification of fragments of first-order logic, we study the complexity of the satisfiability problem for several ordered fragments of first-order logic, which are obtained from the…
We indicate a way of distinguishing between structures, for which, we call two structures distinguishable. Roughly, being distinguishable means that they differ in the number of realizations each gives for some formula. Being…