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Several applied problems are characterized by the need to numerically solve equations with an operator function (matrix function). In particular, in the last decade, mathematical models with a fractional power of an elliptic operator and…
We present a proof procedure for univariate real polynomial problems in Isabelle/HOL. The core mathematics of our procedure is based on univariate cylindrical algebraic decomposition. We follow the approach of untrusted certificates,…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity.…
In this paper we investigate the following existence problem for rational functions: for a given collection $\Pi$ of partitions of a number $n$ to define whether there exists a rational function $f$ of degree $n$ for which $\Pi$ is the…
We develop algebro-combinatorial tools for computing the Thom polynomials for the Morin singularities $A_i(-)$ ($i\ge 0$). The main tool is the function $F^{(i)}_r$ defined as a combination of Schur functions with certain numerical…
Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean…
A classical question of propositional logic is one of the shortest proof of a tautology. A related fundamental problem is to determine the relative efficiency of standard proof systems, where the relative complexity is measured using the…
We present a new tool to compute the number $\phi_\A (\b)$ of integer solutions to the linear system $$ \x \geq 0 \qquad \A \x = \b $$ where the coefficients of $\A$ and $\b$ are integral. $\phi_\A (\b)$ is often described as a \emph{vector…
By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
We derive an identity for certain linear combinations of polylogarithm functions with negative exponents, which implies relations for linear combinations of Eulerian numbers. The coefficients of our linear combinations are related to…
This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that adhere to certain fixed-parameter tractability…
We study a functional equation whose unknown maps a Euclidean space into the space of probability distributions on [0,1]. We prove existence and uniqueness of its solution under suitable regularity and boundary conditions, we show that it…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
Lately, there have been intensive studies on strengths and limitations of nonuniform families of promise decision problems solvable by various types of polynomial-size finite automata families, where ``polynomial-size'' refers to the…
Neural wave functions accomplished unprecedented accuracies in approximating the ground state of many-electron systems, though at a high computational cost. Recent works proposed amortizing the cost by learning generalized wave functions…
In an earlier article [3], we presented an algorithm that can be used to rigorously check whether a specific cosine or sine polynomial is nonnegative in a given interval or not. The algorithm proves to be an indispensable tool in…
Borrowing inspiration from Marcone and Mont\'{a}lban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an…
Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…