Related papers: A Theoretical Review on Solving Algebra Problems
Answer set programming (ASP) is a logic programming paradigm that can be used to solve complex combinatorial search problems. Aggregates are an ASP construct that plays an important role in many applications. Defining a satisfactory…
The goal of text ranking is to generate an ordered list of texts retrieved from a corpus in response to a query. Although the most common formulation of text ranking is search, instances of the task can also be found in many natural…
The application of contemporary artificial intelligence techniques to address geometric problems and automated deductive proof has always been a grand challenge to the interdiscipline field of mathematics and artificial Intelligence. This…
We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it…
Artificial Intelligence (AI) is starting to transform the research process as we know it by automating the discovery of new solutions. Given a task, the typical AI-driven approach is (i) to generate a set of diverse solutions, and then (ii)…
A common technique for checking properties of complex state machines is to build a finite abstraction then check the property on the abstract system -- where a passing check on the abstract system is only transferred to the original system…
Nieuwenhuis, Oliveras, and Tinelli (2006) showed how to describe enhancements of the Davis-Putnam-Logemann-Loveland algorithm using transition systems, instead of pseudocode. We design a similar framework for several algorithms that…
We propose an end-to-end approach for Answer Set Programming (ASP) and linear algebraically compute stable models satisfying given constraints. The idea is to implement Lin-Zhao's theorem together with constraints directly in vector spaces…
The most efficient automated way to construct a large class of quantum photonic experiments is via abstract representation of graphs with certain properties. While new directions were explored using Artificial intelligence and SAT solvers…
Semantic Textual Similarity (STS) research has expanded rapidly since 2021, driven by advances in transformer architectures, contrastive learning, and domain-specific techniques. This survey reviews progress across six key areas:…
The task of artificial intelligence is to provide representation techniques for describing problems, as well as search algorithms that can be used to answer our questions. A widespread and elaborated model is state-space representation,…
As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this paper, we analyze sessions with ChatGPT around topics in basic Linear Algebra. We reflect the…
State transition algorithm (STA) has been emerging as a novel stochastic method for global optimization in recent few years. To make better understanding of continuous STA, a matlab toolbox for continuous STA has been developed. Firstly,…
We present a new approach to enhancing Answer Set Programming (ASP) with Constraint Processing techniques which allows for solving interesting Constraint Satisfaction Problems in ASP. We show how constraints on finite domains can be…
We present algebraic techniques to analyze state space models in the areas of structural identifiability, observability, and indistinguishability. While the emphasis is on surveying existing algebraic tools for studying ODE systems, we also…
Answer set programming (ASP) with disjunction offers a powerful tool for declaratively representing and solving hard problems. Many NP-complete problems can be encoded in the answer set semantics of logic programs in a very concise and…
The Stable Roommates problem (SR) is characterized by the preferences of agents over other agents as roommates: each agent ranks all others in strict order of preference. A solution to SR is then a partition of the agents into pairs so that…
{log} ('setlog') is a satisfiability solver for formulas of the theory of finite sets and finite set relation algebra (FSTRA). As such, it can be used as an automated theorem prover (ATP) for this theory. {log} is able to automatically…
Table reasoning, a task to answer questions by reasoning over data presented in tables, is an important topic due to the prevalence of knowledge stored in tabular formats. Recent solutions use Large Language Models (LLMs), exploiting the…
The Heisenberg algebra is first deformed with the set of parameters ${q, l, \lambda}$ to generate a new family of generalized coherent states. In this framework, the matrix elements of relevant operators are exactly computed. A proof on…