Related papers: Connecting Gr\"obner Bases Programs with Coq to do…

We present a symbolic tool that provides robust algebraic methods to handle automatic deduction tasks for a dynamic geometry construction. The main prototype has been developed as two different worksheets for the open source computer…

There is an ongoing effort to find quantum speedups for learning problems. Recently, [Y. Liu et al., Nat. Phys. $\textbf{17}$, 1013--1017 (2021)] have proven an exponential speedup for quantum support vector machines by leveraging the…

Formally verifying system properties is one of the most effective ways of improving system quality, but its high manual effort requirements often render it prohibitively expensive. Tools that automate formal verification, by learning from…

Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…

Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers…

We develop a method for evaluation of A. Einstein's strength of systems of partial differential and difference equations based on the computation of Hilbert-type dimension polynomials of the associated differential and difference field…

Quantum computing holds the potential to provide speedups in solving complex problems that are currently difficult for classical computers. However, the realization of this potential is hindered by the issue of current hardware reliability,…

In this paper we give a computer proof of a new polynomial identity, which extends a recent result of Alladi and the first author. In addition, we provide computer proofs for new finite analogs of Jacobi and Euler formulas. All computer…

Formally reasoning about functional programs is supposed to be straightforward and elegant, however, it is not typically done as a matter of course. Reasoning in a proof assistant requires "reimplementing" the code in those tools, which is…

In this paper we describe an efficient involutive algorithm for constructing Groebner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain…

We describe an embedding of the QWIRE quantum circuit language in the Coq proof assistant. This allows programmers to write quantum circuits using high-level abstractions and to prove properties of those circuits using Coq's theorem proving…

Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are…

We target the problem of provably computing the equivalence between two complex expression trees. To this end, we formalize the problem of equivalence between two such programs as finding a set of semantics-preserving rewrite rules from one…

Symbolic computation for systems of differential equations is often computationally expensive. Many practical differential models have a form of polynomial or rational ODE system with specified outputs. A basic symbolic approach to analyze…

Faugere's F5 algorithm is one of the fastest known algorithms for the computation of Grobner bases. So far only the F5 Criterion is proved, whereas the second powerful criterion, the Rewritten Criterion, is not understood very well until…

We present a novel approach to non-convex optimization with certificates, which handles smooth functions on the hypercube or on the torus. Unlike traditional methods that rely on algebraic properties, our algorithm exploits the regularity…

Multiobjective discrete programming is a well-known family of optimization problems with a large spectrum of applications. The linear case has been tackled by many authors during the last years. However, the polynomial case has not been…

In this paper we examine the potential of computer-assisted proof methods to be applied much more broadly than commonly recognized. More specifically, we contend that there are vast opportunities to derive useful mathematical results and…

In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…

Quorum systems are a key mathematical abstraction in distributed fault-tolerant computing for capturing trust assumptions. A quorum system is a collection of subsets of all processes, called quorums, with the property that each pair of…