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| home [2026-08-10] – [Mission] Martin Ziegler | home [2026-08-10] (current) – [Mission] Martin Ziegler |
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| Coding theory of discrete data is well-established since Claude Shannon’s famous work. | Coding theory of discrete data is well-established since Claude Shannon’s famous work. |
| Encoding real numbers as infinite sequences of bits is non-trivial: the binary expansion for example renders addition uncomputable. | Encoding real numbers as infinite sequences of bits is non-trivial: the binary expansion for example renders addition uncomputable. |
| * Matthias Schröder has made [[https://dblp.org/pid/12/7010.html|important contributions]] to the qualitative coding theory of continuous data. | * Matthias Schröder has made [[https://dblp.org/pid/12/7010.html|important contributions]] to the qualitative coding theory of continuous data. [[https://www.donghyunlim.com/|Donghyun Lim]] in [[https://library.kaist.ac.kr/search/ctlgSearch/posesn/view.do?bibctrlno=875473|his MSc Thesis]] has investigated quantitative properties of encoding abstract (such as function) spaces; see also the preprint [[https://arxiv.org/abs/2002.04005|arXiv:2002.04005]] and the journal version [[https://doi.org/10.1145/3705609|doi:10.1145/3705609]]. |
| [[https://www.donghyunlim.com/|Donghyun Lim]] in [[https://library.kaist.ac.kr/search/ctlgSearch/posesn/view.do?bibctrlno=875473|his MSc Thesis]] has investigated quantitative properties of encoding abstract (such as function) spaces; see also the extended/journal version [[https://doi.org/10.1145/3705609|doi:10.1145/3705609]] | |
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| see also the [[https://arxiv.org/abs/2002.04005|preprint arXiv:2002.04005]]. | * [[https://www.comp.nus.edu.sg/programmes/pg/phdcs/directory/|Ivan Koswara]] and [[http://www.lix.polytechnique.fr/Labo/Gleb.POGUDIN/|Gleb Pogudin]] and [[https://www.researchgate.net/profile/Svetlana-Selivanova|Svetlana Selivanova]] have [[http://cs4contidat.eu/yjcom101727.pdf|related the bit-complexity intrinsic to approximate solutions of linear partial differential equations]] to discrete complexity classes #P and PSPACE. This complements [[https://doi.org/10.1007/s00037-010-0286-0|investigations]] of ordinary but non-linear differential equations. |
| * [[https://www.comp.nus.edu.sg/programmes/pg/phdcs/directory/|Ivan Koswara]] and [[http://www.lix.polytechnique.fr/Labo/Gleb.POGUDIN/|Gleb Pogudin]] and [[https://www.researchgate.net/profile/Svetlana-Selivanova|Svetlana Selivanova]] have [[http://cs4contidat.eu/yjcom101727.pdf|related the bit-complexity intrinsic to approximate solutions of linear partial differential equations]] to discrete complexity classes #P and PSPACE. | |
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| * [[http://informatik.uni-trier.de/~brausse/personal/index.xhtml|Franz Brauße]] and [[https://www.maastrichtuniversity.nl/pieter.collins|Pieter Collins]] envision a Computer <del>Algebra</del>//Analysis// System | * Previous works [[http://doi.org/10.1137/S0097539794263452|doi:10.1137/S0097539794263452]] and [[http://doi.org/10.1145/2189778.2189780|doi:10.1145/2189778.2189780]] have generalized classical polynomials to higher types, such as operators in analysis, in terms of so-called second-order polynomials. The degree subclassifies ordinary polynomial growth into linear, quadratic, cubic etc. In order to similarly classify second-order polynomials, [[https://doi.org/10.4230/LIPIcs.FSTTCS.2025.42|doi:10.4230/LIPIcs.FSTTCS.2025.42]] defines their degree to be an 'arctic' first-order polynomial (namely a term/expression over variable D and operations + and × and max). This degree turns out to transform as nicely under (now two kinds of) polynomial composition as the ordinary one. We also establish a normal form and semantic uniqueness for second-order polynomials. Then we define the degree of a third-order polynomial to be an arctic second-order polynomial, and establish its transformation under three kinds of composition. |
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| | * [[https://doi.org/10.1007/978-3-032-31348-5_9|What is a polynomial-time computable L^2 (aka square-integrable) function?]] Finding a 'good' definition is prerequisite to complexity investigations of partial differential equations beyond classical solutions [[https://doi.org/10.23638/LMCS-13(3:21)2017|doi:10.23638/LMCS-13(3:21)2017]]; see also [[https://doi.org/10.1007/978-3-032-09645-6_2|doi:10.1007/978-3-032-09645-6_2]]. |
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| | * [[http://informatik.uni-trier.de/~brausse/personal/index.xhtml|Franz Brauße]] and [[https://www.maastrichtuniversity.nl/pieter.collins|Pieter Collins]] envision a Computer <del>Algebra</del>//Analysis// [[https://doi.org/10.1007/978-3-031-14788-3_5|System]]. |
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| | * [[https://www.b-tu.de/fg-theoretische-informatik/team/lehrstuhlinhaber|Klaus Meer]] initiates [[https://doi.org/10.1007/978-3-031-63742-1_5|Software Testing in Computable Analysis]]. |
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| ===== References ===== | ===== References ===== |