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seminars [2021-04-27] – Svetlana Selivanova | seminars [2022-06-02] – [Computing with Infinite Objects via Coinductive Definitions] Martin Ziegler | ||
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====== Seminar on Theoretical Computer Science, Logic, and Real Computation ====== | ====== Seminar on Theoretical Computer Science, Logic, and Real Computation ====== | ||
+ | * [[Seminars# | ||
* [[Seminars# | * [[Seminars# | ||
* [[Seminars# | * [[Seminars# | ||
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* [[Seminars# | * [[Seminars# | ||
+ | ===== 2022 ===== | ||
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+ | ====Computing with Infinite Objects via Coinductive Definitions==== | ||
+ | * June 2, 14h30 KST | ||
+ | * Dieter Spreen (U Siegen) | ||
+ | |||
+ | // | ||
+ | A representation-free logic-base approach for computing with infinite objects will be presented. The logic is intuitionistic first-order logic extended by strictly positive inductive and coinductive definitions. Algorithms can be extracted from proofs via realizability. The approach allows to deal with objects like the real numbers and nonempty compact sets of such. More general, it allows to deal with compact metric spaces that come equipped with a finite set of contractions such that the union of their ranges covers the space, and with continuous maps between such spaces. The computational power of the approach is equivalent to that of type-two theory of effectivity. | ||
+ | |||
+ | {{http:// | ||
===== 2021 ===== | ===== 2021 ===== | ||
- | Currently | + | |
+ | |||
+ | ====Book Review " | ||
+ | * July 9, 16h00, | ||
+ | * Lwam Z. Araya (KAIST) | ||
+ | |||
+ | Abstract: | ||
+ | //Governing the Commons: The Evolution of Institutions for Collective Action// is an examination of the nature of the commons, and the evolution and development of self-organisation and self-governance of those commons. //The Evolution of Institutions | ||
+ | |||
+ | ====Lazy types in iRRAM and computability of Mandelbrot set==== | ||
+ | * May 6, 16h00, via Zoom | ||
+ | * Jihoon Hyun (KAIST) | ||
+ | |||
+ | Abstract: iRRAM iterates all over if more precision is needed. In other words, iRRAM iterates all over even if only a few parts of the program need extra precision. And if that expensively-calculated expression is actually not used in the program, for example by the use of choose function, it will be a waste of computational resources. Although iRRAM has implemented LAZY_BOOLEAN, | ||
+ | |||
+ | Mandelbrot set is a set of complex numbers whose exterior is computably enumerable. There is a conjecture which says that the Mandelbrot set is also computably enumerable. I will mention some facts about the set, and explain what I have done with iRRAM to draw the set on a plane. | ||
====Introduction to mathematical Ludology==== | ====Introduction to mathematical Ludology==== | ||
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* Hyunwoo Lee (KAIST) | * Hyunwoo Lee (KAIST) | ||
- | Abstract: Game is a part of human life from the ancient times. However, there were only few attempts to study games using mathematics. Although there is the academic field called game theory, the notion of the game in game theory is bit different from the game which we really play in regular life. Another attempt is using narratology, | + | Abstract: Game is a part of human life from ancient times. However, there were only a few attempts to study games using mathematics. Although there is the academic field called game theory, the notion of the game in game theory is a bit different from the game which we really play in regular life. Another attempt is using narratology, |
In this talk, I introduce a young academic discipline called Ludology, especially mathematical Ludology which studies and analyzes the game ' | In this talk, I introduce a young academic discipline called Ludology, especially mathematical Ludology which studies and analyzes the game ' | ||
- | ====Introduction to Riemannian Geometry, Part IV==== | + | ====Introduction to Riemannian Geometry, Part IV and V==== |
* Apr 1, 16h00, via Zoom | * Apr 1, 16h00, via Zoom | ||
* Apr 22, 16h00, via Zoom (continued) | * Apr 22, 16h00, via Zoom (continued) |