Related papers: Unification and Logarithmic Space
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…
We analytically derive the geometrical structure of the weight space in multilayer neural networks (MLN), in terms of the volumes of couplings associated to the internal representations of the training set. Focusing on the parity and…
In physics, Lie groups represent the algebraic structure that describes symmetry transformations of a given system. Then, the descending Lie algebra of those groups are necessarily real. In most cases, the complexification of those Lie…
Many clustering problems in computer vision and other contexts are also classification problems, where each cluster shares a meaningful label. Subspace clustering algorithms in particular are often applied to problems that fit this…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We will find a lower bound on the recognition complexity of the theories that are nontrivial relative to some equivalence relation (this relation may be equality), namely, each of these theories is consistent with the formula, whose sense…
We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear…
Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
Systems of equations with sets of integers as unknowns are considered. It is shown that the class of sets representable by unique solutions of equations using the operations of union and addition $S+T=\makeset{m+n}{m \in S, \: n \in T}$ and…
{log} (read 'setlog') was born as a Constraint Logic Programming (CLP) language where sets and binary relations are first-class citizens, thus fostering set programming. Internally, {log} is a constraint satisfiability solver implementing…
Given an algebraic structure on the homology of a chain complex, we define its realization space as a Kan complex whose vertices are the structures up to homotopy realizing this structure at the homology level. Our algebraic structures are…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
We consider the class of finitely generated groups which have a normal form computable in logspace. We prove that the class of such groups is closed under finite extensions, finite index subgroups, direct products, wreath products, and also…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
The description complexity of a model is the length of the shortest formula that defines the model. We study the description complexity of unary structures in first-order logic FO, also drawing links to semantic complexity in the form of…