Related papers: A fully automatic problem solver with human-style …
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
Problems in program analysis can be solved by developing novel program semantics and deriving abstractions conventionally. For over thirty years, higher-order program analysis has been sold as a hard problem. Its solutions have required…
Solving mathematical word problems (MWPs) automatically is challenging, primarily due to the semantic gap between human-readable words and machine-understandable logics. Despite the long history dated back to the1960s, MWPs have regained…
This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
Drori et al. (2022) report that "A neural network solves, explains, and generates university math problems by program synthesis and few-shot learning at human level ... [It] automatically answers 81\% of university-level mathematics…
Program synthesis techniques offer significant new capabilities in searching for programs that satisfy high-level specifications. While synthesis has been thoroughly explored for input/output pair specifications (programming-by-example),…
Automated math word problem solvers based on neural networks have successfully managed to obtain 70-80\% accuracy in solving arithmetic word problems. However, it has been shown that these solvers may rely on superficial patterns to obtain…
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…
Mathematical software systems are becoming more and more important in pure and applied mathematics in order to deal with the complexity and scalability issues inherent in mathematics. In the last decades we have seen a cambric explosion of…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
Ever increasing computational power will require methods for automatic programming. We present an alternative to genetic programming, based on a general model of thinking and learning. The advantage is that evolution takes place in the…
The paper discusses the capacities and limitations of current artificial intelligence (AI) technology to solve word problems that combine elementary knowledge with commonsense reasoning. No existing AI systems can solve these reliably. We…
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…
A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
When giving automated feedback to a student working on a beginner's exercise, many programming tutors run into a completeness problem. On the one hand, we want a student to experiment freely. On the other hand, we want a student to write…
Models of complicated systems can be represented in different ways - in scientific papers, they are represented using natural language text as well as equations. But to be of real use, they must also be implemented as software, thus making…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…