Related papers: Derived terms without derivation a shifted perspec…
Kaltofen has proposed a new approach in 1992 for computing matrix determinants without divisions. The algorithm is based on a baby steps/giant steps construction of Krylov subspaces, and computes the determinant as the constant term of a…
We construct a complex entire function with arbitrary number of variables which has the following property: The infinite set consisting of all the values of all its partial derivatives of any orders at all algebraic points, including zero…
Based on a class of associative algebras with zero-divisors which are called real-like algebras by us, we introduce a way of defining automatic differentiation and present different ways of doing automatic differentiation to compute the…
Regular expressions are often ambiguous. We present a novel method based on Brzozowski's derivatives to aid the user in diagnosing ambiguous regular expressions. We introduce a derivative-based finite state transducer to generate parse…
A computationally efficient reformulation of the rigid tube model predictive control is developed. A unique feature of the derived formulation is the utilization of the implicit set representations. This novel formulation does not require…
We consider an equation of multiple variables in which a partial derivative does not vanish at a point. The implicit function theorem provides a local existence and uniqueness of the function for the equation. In this paper, we propose an…
In this letter we present a procedure for the calculation of the Casimir functions of finite-dimensional Poisson systems which avoids the burden of solving a set of partial differential equations, as it is usually suggested in the…
The theory of abstract argumentation frameworks (afs) has, in the main, focused on finite structures, though there are many significant contexts where argumentation can be regarded as a process involving infinite objects. To address this…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
This article shows a very elementary and straightforward proof of the Implicit Function Theorem for differentiable maps $F(x,y)$ defined on a finite-dimensional Euclidean space. There are no hypothesis on the continuity of the partial…
The clausal logical consequences of a formula are called its implicates. The generation of these implicates has several applications, such as the identification of missing hypotheses in a logical specification. We present a procedure that…
If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…
We propose a new grammar-based language for defining information-extractors from documents (text) that is built upon the well-studied framework of document spanners for extracting structured data from text. While previously studied…
The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton…
Several abstract machines that operate on symbolic input alphabets have been proposed in the last decade, for example, symbolic automata or lattice automata. Applications of these types of automata include software security analysis and…
In this work derivations of definite integrals listed in Prudnikov volume I, Gradshteyn and Ryzhik and a few other tables are produced. Special cases of these integrals in terms of fundamental constants are also evaluated. The method used…
We describe an automated method for identifying classes of morphologically related words in an on-line dictionary, and for linking individual senses in the derived form to one or more senses in the base form by means of morphological…
This paper introduces abstractions that are meaningful for computers and that can be built and used according to computers' own criteria, i.e., computable abstractions. It is analyzed how abstractions can be seen to serve as the building…
In this work, we propose a data-driven approach for the construction of finite abstractions (a.k.a., symbolic models) for discrete-time deterministic control systems with unknown dynamics. We leverage notions of so-called alternating…
Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions,…