Related papers: A fully automatic problem solver with human-style …
Plotting solution sets for particular equations may be complicated by the existence of turning points. Here we describe an algorithm which not only overcomes such problematic points, but does so in the most general of settings. Applications…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
Cognitive systems generally require a human to translate a problem definition into some specification that the cognitive system can use to attempt to solve the problem or perform the task. In this paper, we illustrate that large language…
A general quantum algorithm for solving a problem is discussed. The number of steps required to solve a problem using this method is independent of the number of cases that has to be considered classically. Hence, it is more efficient than…
In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…
There is increasing interest in employing large language models (LLMs) as cognitive models. For such purposes, it is central to understand which properties of human cognition are well-modeled by LLMs, and which are not. In this work, we…
This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large…
In a broad sense, artificial intelligence is a service to find a solution to complex intellectual problems. In this sense, the MathPartner service provides artificial intelligence that allows us to formulate questions and receive answers to…
Parametric linear programming is central in polyhedral computations and in certain control applications.We propose a task-based scheme for parallelizing it, with quasi-linear speedup over large problems.
This paper describes a generalization of Clark's completion that is applicable to logic programs containing arithmetic operations and produces syntactically simple, natural looking formulas. If a set of first-order axioms is equivalent to…
Solving math word problems is a challenging task that requires accurate natural language understanding to bridge natural language texts and math expressions. Motivated by the intuition about how human generates the equations given the…
The work we describe here is a part of a research program of developing foundations of declarative solving of search problems. We consider the model expansion task as the task representing the essence of search problems where we are given…
Previous math word problem solvers following the encoder-decoder paradigm fail to explicitly incorporate essential math symbolic constraints, leading to unexplainable and unreasonable predictions. Herein, we propose Neural-Symbolic Solver…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done…
We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…
An original approach to solving rather difficult probabilistic problems arising in studying the readout of random discrete fields and having no exact analytical solutions at the moment is proposed. Several algorithms for direct, iterative,…