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An assignment problem arises when there exists a set of tasks that must be allocated to a set of agents. The bottleneck assignment problem (BAP) has the objective of minimising the most costly allocation of a task to an agent. Under certain…
Multi-task learning, as it is understood nowadays, consists of using one single model to carry out several similar tasks. From classifying hand-written characters of different alphabets to figuring out how to play several Atari games using…
We present a new method for the constraint-based synthesis of termination arguments for linear loop programs based on linear ranking templates. Linear ranking templates are parametrized, well-founded relations such that an assignment to the…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Law-invariant functionals are central to risk management and assign identical values to random prospects sharing the same distribution under an atomless reference probability measure. This measure is typically assumed fixed. Here, we adopt…
This paper shows, in the framework of the logical method,the unsolvability of $k$-set agreement task by devising a suitable formula of epistemic logic. The unsolvability of $k$-set agreement task is a well-known fact, which is a direct…
Contact can be conceptualized as a set of constraints imposed on two bodies that are interacting with one another in some way. The nature of a contact, whether a point, line, or surface, dictates how these bodies are able to move with…
Let $A \cong k\langle X \rangle / I$ be an associative algebra. A finite word over alphabet $X$ is $I${\it-reducible} if its image in $A$ is a $k$-linear combination of length-lexicographically lesser words. An {\it obstruction} in a…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
In [Incer Romeo, I. X., \textit{The Algebra of Contracts}. Ph.D. Thesis, UC Berkeley (2022)] an algebraic perspective on assume-guarantee contracts is proposed. This proposal relies on a construction involving Boolean algebras. However, the…
We study the problem of enumerating answers of Conjunctive Queries ranked according to a given ranking function. Our main contribution is a novel algorithm with small preprocessing time, logarithmic delay, and non-trivial space usage during…
Algebraic operations are understood as topologiztion of algebra. They become an example of simplest convergence space. In our article the convergence is a arbitrary multivalued appointment. The continuity of some mapping between two…
An order is a commutative ring that as an abelian group is finitely generated and free. A commutative ring is reduced if it has no non-zero nilpotent elements. In this paper we use a new tool, namely, the fact that every reduced order has a…
The recent approaches of extending the GRAPHPLAN algorithm to handle more expressive planning formalisms raise the question of what the formal meaning of "expressive power" is. We formalize the intuition that expressive power is a measure…
The famous asynchronous computability theorem (ACT) relates the existence of an asynchronous wait-free shared memory protocol for solving a task with the existence of a simplicial map from a subdivision of the simplicial complex…
Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
We formulate and prove a very general relative version of the Dobrushin-Lanford-Ruelle theorem which gives conditions on constraints of configuration spaces over a finite alphabet such that for every absolutely summable relative…
Multimedia applications often require concurrent solutions to multiple tasks. These tasks hold clues to each-others solutions, however as these relations can be complex this remains a rarely utilized property. When task relations are…
We provide an expository account of some of the Hopf algebras that can be defined using trees, labeled trees, ordered trees and heap ordered trees. We also describe some actions of these Hopf algebras on algebra of functions.
Process algebra and temporal logic are two popular paradigms for the specification, verification and systematic development of reactive and concurrent systems. These two approaches take different standpoint for looking at specifications and…