Related papers: Code Equivalence, Point Set Equivalence, and Polyn…
In this paper we consider the classical problem of computing linear extensions of a given poset which is well known to be a difficult problem. However, in our setting the elements of the poset are multivariate polynomials, and only a small…
This note addresses the issue as to which ceers can be realized by word problems of computably enumerable (or, simply, c.e.) structures (such as c.e. semigroups, groups, and rings), where being realized means to fall in the same…
Achieving backward compatibility when rolling out new models can highly reduce costs or even bypass feature re-encoding of existing gallery images for in-production visual retrieval systems. Previous related works usually leverage losses…
We study the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for cyclotomic number fields,namely: we prove that both problems are equivalent via a polynomial noise increase as long as the…
We contribute to the program of extending computable structure theory to the realm of metric structures by investigating lowness for isometric isomorphism of metric structures. We show that lowness for isomorphism coincides with lowness for…
Linear logic Concurrent Constraint programming (LCC) is an extension of concurrent constraint programming (CC) where the constraint system is based on Girard's linear logic instead of the classical logic. In this paper we address the…
We consider a problem that involves finding similar elements in a collection of sets. The problem is motivated by applications in machine learning and pattern recognition. We formulate the similar elements problem as an optimization and…
The paper introduces the simultaneous partial-inverse problem (SPI) for polynomials and develops its application to decoding interleaved Reed--Solomon codes beyond half the minimum distance. While closely related both to standard key…
We claimed that there is a polynomial algorithm to test if two graphs are isomorphic. But the algorithm is wrong. It only tests if the adjacency matrices of two graphs have the same eigenvalues. There is a counterexample of two…
We propose a generalization of logarithmic and Schwarzenberger bundles over $\P^n=\P^n(\C)$ when the rank is greater than $n$. The first ones are associated to finite sets of points on $\P^{n\vee}$ and the second ones to curves with degree…
In mutation testing the question whether a mutant is equivalent to its program is important in order to compute the correct mutation score. Unfortunately, answering this question is not always possible and can hardly be obtained just by…
The computational complexity of the graph isomorphism problem is considered to be a major open problem in theoretical computer science. It is known that testing isomorphism of chordal graphs is polynomial-time equivalent to the general…
We apply the theory of Lie point symmetries for the study of a family of partial differential equations which are integrable by the hyperbolic reductions method and are reduced to members of the Painlev\'{e} transcendents. The main results…
A classical measure of string comparison is given by the longest common subsequence (LCS) problem on a pair of strings. We consider its generalisation, called the semi-local LCS problem, which arises naturally in many string-related…
Detecting objects and estimating their pose remains as one of the major challenges of the computer vision research community. There exists a compromise between localizing the objects and estimating their viewpoints. The detector ideally…
A graph is said to be circular-arc if the vertices can be associated with arcs of a circle so that two vertices are adjacent if and only if the corresponding arcs overlap. It is proved that the isomorphism of circular-arc graphs can be…
Symbolic regression plays a crucial role in modern scientific research thanks to its capability of discovering concise and interpretable mathematical expressions from data. A key challenge lies in the search for parsimonious and…
A set of vertices in a graph is c-colorable if the subgraph induced by the set has a proper c-coloring. In this paper, we study the problem of finding a step-by-step transformation (reconfiguration) between two c-colorable sets in the same…
We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…
Graph Isomorphism (GI) is a fundamental algorithmic problem. Amongst graph classes for which the computational complexity of GI has been resolved, trees are arguably the most fundamental. Tree Isomorphism is complete for deterministic…