Related papers: Symbolic Computation for All the Fun
We use SMT technology to address a class of problems involving uninterpreted functions and nonlinear real arithmetic. In particular, we focus on problems commonly found in mathematical competitions, such as the International Mathematical…
We present FIMO, an innovative dataset comprising formal mathematical problem statements sourced from the International Mathematical Olympiad (IMO) Shortlisted Problems. Designed to facilitate advanced automated theorem proving at the IMO…
The International Mathematical Olympiad (IMO) is perhaps the most celebrated mental competition in the world and as such is among the greatest grand challenges for Artificial Intelligence (AI). The IMO Grand Challenge, recently formulated,…
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…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…
Satisfiability Modulo Counting (SMC) encompasses problems that require both symbolic decision-making and statistical reasoning. Its general formulation captures many real-world problems at the intersection of symbolic and statistical…
Simulation Optimization (SO) refers to the optimization of an objective function subject to constraints, both of which can be evaluated through a stochastic simulation. To address specific features of a particular simulation---discrete or…
Combinatorial optimization problems are computationally hard in general, but they are ubiquitous in our modern life. A coherent Ising machine (CIM) based on a multiple-pulse degenerate optical parametric oscillator (DOPO) is an alternative…
Satisfiability Modulo Counting (SMC) is a recently proposed general language to reason about problems integrating statistical and symbolic Artificial Intelligence. An SMC problem is an extended SAT problem in which the truth values of a few…
Symbolic equations are one of the many representations used in physics. Understanding these representations is important for students because they are how students access knowledge in physics. In this paper I build off of the work by Redish…
A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…
Let a quantified inequality constraint over the reals be a formula in the first-order predicate language over the structure of the real numbers, where the allowed predicate symbols are $\leq$ and $<$. Solving such constraints is an…
Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data…
In this paper, we propose a novel approach for solving linear numeric planning problems, called Symbolic Pattern Planning. Given a planning problem $\Pi$, a bound $n$ and a pattern -- defined as an arbitrary sequence of actions -- we encode…
In this paper we consider a scenario where there are several algorithms for solving a given problem. Each algorithm is associated with a probability of success and a cost, and there is also a penalty for failing to solve the problem. The…
We present AMO-Bench, an Advanced Mathematical reasoning benchmark with Olympiad level or even higher difficulty, comprising 50 human-crafted problems. Existing benchmarks have widely leveraged high school math competitions for evaluating…
As large language models (LLMs) reach high scores on established mathematical benchmarks, such as GSM8K and MATH, the research community has turned to International Mathematical Olympiad (IMO) problems to push the evaluation frontier.…