Related papers: On two-variable guarded fragment logic with expres…
We construct Borel graphs which settle several questions in descriptive graph combinatorics. These include "Can the Baire measurable chromatic number of a locally finite Borel graph exceed the usual chromatic number by more than one?" and…
The two--dimensional topological BF model is quantized in the axial gauge. We show that this theory is trivially ultraviolet finite and that the usual infrared problem of the propagator of the scalar field in two dimensions is replaced by…
We demonstrate that certain Johnson-type bounds are asymptotically exact for a variety of classes of codes, namely, constant-composition codes, nonbinary constant-weight codes and multiply constant-weight codes. This was achieved via an…
We investigate the statistical properties of cut sizes generated by heuristic algorithms which solve approximately the graph bisection problem. On an ensemble of sparse random graphs, we find empirically that the distribution of the cut…
We investigate the complexity of satisfiability for finite-variable fragments of propositional dynamic logics. We consider three formalisms belonging to three representative complexity classes, broadly understood,---regular PDL, which is…
We consider the complexity of the open-world query answering problem, where we wish to determine certain answers to conjunctive queries over incomplete datasets specified by an initial set of facts and a set of guarded TGDs. This problem…
Many load balancing problems that arise in scientific computing applications ask to partition a graph with weights on the vertices and costs on the edges into a given number of almost equally-weighted parts such that the maximum boundary…
Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms using semidefinite programming (SDP) to compute this constant…
We extend the inflationary fixed-point logic, IFP, with a new kind of second-order quantifiers which have (poly-)logarithmic bounds. We prove that on ordered structures the new logic $\exists^{\log^{\omega}}\text{IFP}$ captures the limited…
The color code is a topological quantum error-correcting code supporting a variety of valuable fault-tolerant logical gates. Its two-dimensional version, the triangular color code, may soon be realized with currently available…
Verification of properties of first order logic with two variables FO2 has been investigated in a number of contexts. Over arbitrary structures it is known to be decidable with NEXPTIME complexity, with finitely satisfiable formulas having…
An "edge guard set" of a plane graph $G$ is a subset $\Gamma$ of edges of $G$ such that each face of $G$ is incident to an endpoint of an edge in $\Gamma$. Such a set is said to guard $G$. We improve the known upper bounds on the number of…
We investigate the distance properties of linear locally recoverable codes (LRC codes) with all-symbol locality and availability. New upper and lower bounds on the minimum distance of such codes are derived. The upper bound is based on the…
We prove the following local strengthening of Shearer's classic bound on the independence number of triangle-free graphs: For every triangle-free graph $G$ there exists a probability distribution on its independent sets such that every…
We characterize the languages in the individual levels of the quantifier alternation hierarchy of first-order logic with two variables by identities. This implies decidability of the individual levels. More generally we show that the…
Logical formalisms such as first-order logic (FO) and fixpoint logic (FP) are well suited to express in a declarative manner fundamental graph functionalities required in distributed systems. We show that these logics constitute good…
Graded modal logic is the formal language obtained from ordinary (propositional) modal logic by endowing its modal operators with cardinality constraints. Under the familiar possible-worlds semantics, these augmented modal operators receive…
Given a formula in quantifier-free Presburger arithmetic, if it has a satisfying solution, there is one whose size, measured in bits, is polynomially bounded in the size of the formula. In this paper, we consider a special class of…
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…
A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…