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In the literature on Kleene algebra (KA), a number of variants have been proposed such as Kleene algebra with tests, commutative KA, bi-KA, and concurrent KA. The equational theories of some of these structures have then been studied in the…
Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of…
A classical problem in grammatical inference is to identify a deterministic finite automaton (DFA) from a set of positive and negative examples. In this paper, we address the related - yet seemingly novel - problem of identifying a set of…
We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a…
Our main aim is to apply the theory of regularly varying functions to the asymptotical analysis at infinity of solutions of Friedmann cosmological equations. A new constant $\Gamma$ is introduced related to the Friedmann cosmological…
Numerical solutions for flows in partially saturated porous media pose challenges related to the non-linearity and elliptic-parabolic degeneracy of the governing Richards' equation. Iterative methods are therefore required to manage the…
We describe a framework for systematic enumeration of families combinatorial structures which possess a certain regularity. More precisely, we describe how to obtain the differential equations satisfied by their generating series. These…
Fixed-order perturbative calculations for differential cross sections can suffer from non-physical artifacts: they can be non-positive, non-normalizable, and non-finite, none of which occur in experimental measurements. We propose a…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
Sequence-to-sequence (SEQ2SEQ) models have been successfully applied to automatic math word problem solving. Despite its simplicity, a drawback still remains: a math word problem can be correctly solved by more than one equations. This…
Kleene algebra axioms are complete with respect to both language models and binary relation models. In particular, two regular expressions recognise the same language if and only if they are universally equivalent in the model of binary…
The Rabin tree theorem yields an algorithm to solve the satisfiability problem for monadic second-order logic over infinite trees. Here we solve the probabilistic variant of this problem. Namely, we show how to compute the probability that…
In problem solving, understanding the problem that one seeks to solve is an essential initial step. In this paper, we propose computational methods for facilitating problem understanding through the task of recognizing the unknown in…
In previous literature, backward error analysis was used to find ordinary differential equations (ODEs) approximating the gradient descent trajectory. It was found that finite step sizes implicitly regularize solutions because terms…
A method to the explict solutions of general systems of algebraic equations is presented via the metric form of affiliated K\"ahler manifolds. The solutions to these systems arise from sets of geodesic second order non-linear differential…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
Discontinuity with respect to data perturbations is common in algebraic computation where solutions are often highly sensitive. Such problems can be modeled as solving systems of equations at given data parameters. By appending auxiliary…
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…