Amir Tabatabai and Rahele Jalali visiting

Amir Tabatabai and Rahele Jalali, both PhD students at the Institute of Mathematics of the Czech Academy of Sciences under the supervision of Pavel Pudlak, are visiting Swansea University 13 Nov – 6 Dec 2017. Amir will give a talk on Computational Flows in Arithmetic on 16 November. More information: A computational flow is a pair consisting of a sequence of computational  problems of a certain sort and a sequence of computational reductions among them. In this talk we will explain the basics of the theory of computational flows and how they make a sound and complete interpretation for bounded theories of arithmetic. This property helps us to decompose a first order arithmetical proof to a sequence of computational reductions by which we can extract the computational content of the low complexity statements in some bounded theories of arithmetic such as  .

Arno Pauly joining our department

We would like to welcome Arno Pauly, who has recently joined the computer science department here in Swansea. Today he is going to give a talk on Noncomputability in analysis as a part of our Computational Foundry Seminar Series. More information: Many theorems in analysis state the existence of a certain object depending on some parameter. Each such theorem has an associated computational task: Compute the object from the parameter. From the viewpoint of a constructivist, these tasks are intricately linked to the meaningful truth of the theorems. From a pragmatic perspective, the applicability of a theorem to fields like physics or economics is tied to the solvability of the associated computational task.

Break through result

Oliver Kullmann and his co-authors Marein Heule, and Victor Marek used SAT-solving techniques to solve a long standing open problem in Ramsey Theory known as the Boolean Pythagorean Triples Problem: It is impossible to divide the natural numbers into two parts such that none of the parts contains a Pythagorean triple, that is numbers a,b,c such that a^2+b^2=c^2. In fact, they found a smallest number N (namely N = 7825) such that the set {1,…,N} cannot be divided into two parts as described above. Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek. Solving and Verifying the Boolean Pythagorean Triples Problem via Cube-and-Conquer. In Nadia Creignou and Daniel Le Berre (Ed.), Theory and Applications of Satisfiability Testing – SAT 2016. (pp. 228-245). Springer.



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Computing with Infinite Data EU Horizon 2020 Marie Sklodowska-Curie Research and Innovation Staff Exchange (MSCA-RISE), 4 years, start April 2017, total value 1,462,500 Euros Participating universities Siegen (Germany), Trier(Germany), Munich (Germany), Swansea (UK), Birmingham (UK), INRIA (France), Ljubljana (Slovenia), Maastricht (Netherlands), Stockholm (Sweden), Padova (Italy), Algarve (Portugal), Aston (UK), Dortmund(Germany), KAIST (Korea), JAIST (Japan), Novosibirsk (Russia), UNISA (South-Africa), Andres Bello (Chile), Canterbury (NZ), Cincinnati (USA), Nanyang (Singapore), Abstract The joint research in this programme will study important aspects—both theoretical as well as applied—of computing with infinite objects. A central aim is laying the grounds for the generation of efficient and verified software in engineering applications. A prime example for infinite data is provided by the real numbers, most commonly conceived as infinite sequences of digits. While most applications in science and engineering substitute the reals with floating point numbers of fixed finite precision and thus have to deal with truncation and rounding errors, the approach in this project is different: exact real numbers are taken as first-class citizens and while any computation can only exploit a finite portion of its input in finite time, increased precision is always available by continuing the computation process. This project aims to bring together the expertise of specialists in mathematics, logic, and computer science to push the frontiers of our theoretical and practical understanding of computing with infinite objects. Three overarching motivations drive the proposed collaboration: Representability. Cardinality considerations tell us that it is not possible to represent arbitrary mathematical objects in a way that is accessible to computation. We will enlist expertise in topology, logic, and set theory, to address the question of which objects are representable and how they can be represented most efficiently. Constructivity. Working in a constructive mathematical universe can greatly enhance our understanding of the link between computation and mathematical structure. It not only informs us which are the objects of relevance, it also allows us to devise always correct algorithms from proofs. Efficient implementation. We also aim to make progress on concrete implementations. Theoretical insights from elsewhere will be tested in actual computer systems; obstacles encountered in the latter will inform the direction of mathematical investigation.