Related papers: Conelikes and Ranker Comparisons
The feasibility of a classification-by-rank program for modular categories follows from the Rank-Finiteness Theorem. We develop arithmetic, representation theoretic and algebraic methods for classifying modular categories by rank. As an…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
Many combinatorial optimisation problems hide algebraic structures that, once exposed, shrink the search space and improve the chance of finding the global optimal solution. We present a general framework that (i) identifies algebraic…
The linear ordering problem (LOP), which consists in ordering M objects from their pairwise comparisons, is commonly applied in many areas of research. While efforts have been made to devise efficient LOP algorithms, verification of whether…
This paper proves that a plactic monoid of any finite rank will have decidable first order theory. This resolves other open decidability problems about the finite rank plactic monoids, such as the Diophantine problem and identity checking.…
We investigate the polynomial closure operation (C -> Pol(C)) defined on classes of regular languages. We present an interesting and useful connection relating the separation problem for the class C and the membership problem for it…
We investigate regular realizability (RR) problems, which are the problems of verifying whether intersection of a regular language -- the input of the problem -- and fixed language called filter is non-empty. In this paper we focus on the…
We study the problem of combining the outcomes of several different classifiers in a way that provides a coherent inference that satisfies some constraints. In particular, we develop two general approaches for an important…
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…
The program-over-monoid model of computation originates with Barrington's proof that the model captures the complexity class $\mathsf{NC^1}$. Here we make progress in understanding the subtleties of the model. First, we identify a new…
We study a family of groups consisting of the simplest extensions of lamplighter groups. We use these groups to answer multiple open questions in combinatorial group theory, providing groups that exhibit various combinations of properties:…
In this article, we present a fresh perspective on language, combining ideas from various sources, but mixed in a new synthesis. As in the minimalist program, the question is whether we can formulate an elegant formalism, a universal…
We describe a practical algorithm for computing normal forms for semigroups and monoids with finite presentations satisfying so-called small overlap conditions. Small overlap conditions are natural conditions on the relations in a…
We propose a novel and efficient algorithm for the collaborative preference completion problem, which involves jointly estimating individualized rankings for a set of entities over a shared set of items, based on a limited number of…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
We propose a new numerical algorithm for computing the tensor rank decomposition or canonical polyadic decomposition of higher-order tensors subject to a rank and genericity constraint. Reformulating this computational problem as a system…
We study the membership problem to context-free languages L (CFLs) on probabilistic words, that specify for each position a probability distribution on the letters (assuming independence across positions). Our task is to compute, given a…
We study varieties that contain unranked tree languages over all alphabets. Trees are labeled with symbols from two alphabets, an unranked operator alphabet and an alphabet used for leaves only. Syntactic algebras of unranked tree languages…
The study of the word problems of groups dates back to Dehn in 1911, and has been a central topic of study in both group theory and computability theory. As most naturally occurring presentations of groups are recursive, their word problems…
Covering spaces are a fundamental tool in algebraic topology because of the close relationship they bear with the fundamental groups of spaces. Indeed, they are in correspondence with the subgroups of the fundamental group: this is known as…