Related papers: alphaCertified: certifying solutions to polynomial…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
The Abella interactive theorem prover has proven to be an effective vehicle for reasoning about relational specifications. However, the system has a limitation that arises from the fact that it is based on a simply typed logic:…
This paper presents a methodology for constructing iterative schemes of any order of convergence for solving nonlinear systems of equations. It also provides formulas for the order of convergence of any iterative schemes constructed using…
Existing color sampling based alpha matting methods use the compositing equation to estimate alpha at a pixel from pairs of foreground (F) and background (B) samples. The quality of the matte depends on the selected (F,B) pairs. In this…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
Using polynomial equations to model combinatorial problems has been a popular tool both in computational combinatorics as well as an approach to proving new theorems. In this paper, we look at several combinatorics problems modeled by…
Continuum normalization of echelle spectra is an important data analysis step that is difficult to automate. Polynomial fitting requires a reasonably high order model to follow the steep slope of the blaze function. However, in the presence…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
Because of the probabilistic/nondeterministic behavior of quantum programs, it is highly advisable to verify them formally to ensure that they correctly implement their specifications. Formal verification, however, also traditionally…
We present an executable formally verified SAT encoding of classical AI planning. We use the theorem prover Isabelle/HOL to perform the verification. We experimentally test the verified encoding and show that it can be used for reasonably…
Computer algebra systems are really good at factoring polynomials, i.e. writing f as a product of irreducible factors. It is relatively easy to verify that we have a factorisation, but verifying that these factors are irreducible is a much…
We show that verification of object-oriented programs by means of the assertional method can be achieved in a simple way by exploiting a syntax-directed transformation from object-oriented programs to recursive programs. This transformation…
In this paper, we explore the merits of various algorithms for polynomial optimization problems, focusing on alternatives to sum of squares programming. While we refer to advantages and disadvantages of Quantifier Elimination, Reformulation…
Let M be an archimedean quadratic module of real t-by-t matrix polynomials in n variables, and let S be the set of all real n-tuples where each element of M is positive semidefinite. Our key finding is a natural bijection between the set of…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
In the certification problem, the algorithm is given a function $f$ with certificate complexity $k$ and an input $x^\star$, and the goal is to find a certificate of size $\le \text{poly}(k)$ for $f$'s value at $x^\star$. This problem is in…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and…