Related papers: On the Complexity of Optimization Problems based o…
Several algorithms have been proposed to compute partitions of networks into communities that score high on a graph clustering index called modularity. While publications on these algorithms typically contain experimental evaluations to…
Given the complexity of modern software systems, it is of great importance that such systems be able to autonomously modify themselves, i.e., self-adapt, with minimal human supervision. It is critical that this adaptation both results in…
We introduce a practical method to enforce partial differential equation (PDE) constraints for functions defined by neural networks (NNs), with a high degree of accuracy and up to a desired tolerance. We develop a differentiable…
Answer Set Programming with Quantifiers (ASP(Q)) has been introduced to provide a natural extension of ASP modeling to problems in the polynomial hierarchy (PH). However, ASP(Q) lacks a method for encoding in an elegant and compact way…
Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has…
Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate…
In this work we study preprocessing for tractable problems when part of the input is unknown or uncertain. This comes up naturally if, e.g., the load of some machines or the congestion of some roads is not known far enough in advance, or if…
This work considers a number of optimization problems and reductive relations between them. The two main problems we are interested in are the \emph{Optimal Decision Tree} and \emph{Set Cover}. We study these two fundamental tasks under…
Preference handling and optimization are indispensable means for addressing non-trivial applications in Answer Set Programming (ASP). However, their implementation becomes difficult whenever they bring about a significant increase in…
Knowledge compilation transforms logical theories into circuit representations that support efficient reasoning. We study this problem for propositional groundings of FO2, the two-variable fragment of first-order logic over finite domains.…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The problem of minimizing a polynomial over a set of polynomial inequalities is an NP-hard non-convex problem. Thanks to powerful results from real algebraic geometry, one can convert this problem into a nested sequence of…
Mathematical optimization offers highly-effective tools for finding solutions for problems with well-defined goals, notably scheduling. However, optimization solvers are often unexplainable black boxes whose solutions are inaccessible to…
An automaton is partially ordered if the only cycles in its transition diagram are self-loops. The expressivity of partially ordered NFAs (poNFAs) can be characterized by the Straubing-Th\'erien hierarchy. Level 3/2 is recognized by poNFAs,…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Partially ordered nondeterminsitic finite automata (poNFAs) are NFAs whose transition relation induces a partial order on states, that is, for which cycles occur only in the form of self-loops on a single state. A poNFA is universal if it…
We study the optimization of functions with $n>2$ arguments that have a representation as a sum of several functions that have only $2$ of the $n$ arguments each, termed sums of bivariates, on finite domains. The complexity of optimizing…
A fundamental question in the conjunction of information theory, biophysics, bioinformatics and thermodynamics relates to the principles and processes that guide the development of natural intelligence in natural environments where…