Related papers: Tarski's influence on computer science
We give a selective survey of topics in algebraic deformation theory ranging from its inception to current times. Throughout, the numerous contributions of Murray Gerstenhaber are emphasized, especially the common themes of cohomology,…
In the 1930's, Tarski introduced his plank problem at a time when the field Discrete Geometry was about to born. It is quite remarkable that Tarski's question and its variants continue to generate interest in the geometric and analytic…
The purpose of this paper is to provide a new account of multiplicity for finite morphisms between smooth projective varieties. Traditionally, this has been defined using commutative algebra in terms of the length of integral ring…
The availability of a number of databases, in particular the Science Citation Index (SCI), have encouraged the development and use of bibliometric techniques to analyze and evaluate the production and impact of scientists. To avoid pitfalls…
This is an exposition of the contributions of L\'aszl\'o Lov\'asz to mathematics and computer science written on the occasion of the bestowal of the Abel Prize~2021 to him. Our survey, of course, cannot be exhaustive. We sketch remarkable…
Neural network-based machine learning is capable of approximating functions in very high dimension with unprecedented efficiency and accuracy. This has opened up many exciting new possibilities, not just in traditional areas of artificial…
The following is an exposition of a course of algebra that Prof. Aleksandr Aleksandrovich Zykov (1922-2013) distributed among the participants of his seminar in graph theory not far away from Odessa, Ukraine, on September, 1991. It is a…
The aim of this work is to develop a study from the perspective of Abstract Algebraic Logic of some bilattice-based logical systems introduced in the nineties by Ofer Arieli and Arnon Avron. The motivation for such an investigation has two…
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of…
This is a revised version of the notes from the week-long course I gave at the Centre de Recerca Matematica, Barcelona, in September of 2010. The aim is to give a working overview of recent methods and results in "Blaschkean integral…
Efficient numerical linear algebra is a core ingredient in many applications across almost all scientific and industrial disciplines. With this survey we want to illustrate that numerical linear algebra has played and is playing a crucial…
A new class of noncommutative $k$-algebras (for $k$ an algebraically closed field) is defined and shown to contain some important examples of quantum groups. To each such algebra, a first order theory is assigned describing models of a…
Most if not all of today's revolutionary technologies have a common foundation, namely the intelligent use of information. It is clear that computers play a central role: but the contribution of mathematics, though less visible, is no less…
This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor…
We survey the notion and history of error-correcting codes and the algorithms needed to make them effective in information transmission. We then give some basic as well as more modern constructions of, and algorithms for, error-correcting…
While there has been some discussion on how Symbolic Computation could be used for AI there is little literature on applications in the other direction. However, recent results for quantifier elimination suggest that, given enough example…
The aim of this note is to recast somewhat informal axiom system of quantum mechanics used by physicists (Dirac calculus) in the language of Continuous Logic. We note an analogy between Tarski's notion of cylindric algebras, as a tool of…
Qualitative spatial models based on Goodman-style mereology and pseudo-topology often pose problems for advanced geometric reasoning, as they lack true Euclidean geometry and fully developed topological spaces. We address this issue by…
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations,computer algebra systems are employed. In our research, we have been using Cadabra as the main computer algebra system for several…
We present an overview of some significant results of Thurston and their impact on mathematics. The final version of this paper will appear as Chapter 1 of the book "In the tradition of Thurston: Geometry and topology", edited by K. Ohshika…