Date/Time : 08 Sep 2021 16:00
Venue : via Zoom
Speaker : Bakhadyr Khoussainov / Frank Stephan, UESTC, Chengdu and The University of Auckland, New Zealand / NUS

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Parity games are games where a marker is moved on a finite graph and each node is annotated with a natural number; the game runs forever and the largest number in an infinitely often visited node decides the winner, if it is even then player Anke wins else player Boris wins. Marcin Jurdzinski showed that this game is in UP intersected coUP and also provided the first not fully exponential algorithm for it; however, the exact time complexity remained unresolved. In 2017, Calude, Jain, Khoussainov, Li and Stephan found a quasipolynomial time algorithm which Jurdzinski and Lazic as well as Schewe and his collaborators improved to be in polynomial space as well. The talk provides the way this algorithm was found and the implications it has for the fixed-parameter-tracktability of parity games and related problems like coloured Muller games. Though now quite a number of quasipolynomial time algorithms are known and there is quite extensive research in this topic, the question on whether parity games can even be solved in polynomial time is still unresolved.

This talk is given by Bakhadyr Khoussainov and Frank Stephan jointly also on behalf of their coauthors Cristian Calude, Sanjay Jain and Wei Li.

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Date/Time : 01 Sep 2021 16:00
Venue : via Zoom
Speaker : Rupert Hoelzl, Bundeswehr University Munich

Join Zoom Meeting https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Passcode: 1729=x3+y3 We investigates inductive inference from the perspective of reverse mathematics. Reverse mathematics is a framework that allows gauging the proof strength of theorems and axioms in many areas of mathematics. We apply its methods to basic notions of algorithmic learning theory such as Angluin’s tell-tale criterion and its variants for learning in the limit and for conservative learning, as well as to the more general scenario of partial learning. These notions are studied in the reverse mathematics context for uniformly and weakly represented families of languages. The results are stated in terms of axioms referring to induction strength and to domination of weakly represented families of functions. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

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Date/Time : 25 Aug 2021 16:00
Venue : via Zoom
Speaker : Ng Keng Meng,

Join Zoom Meeting https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Passcode: 1729=x3+y3 There has been a recent revival in the interest in sub-computable mathematics. One of these approaches is to consider “primitive recursive” or punctual structures. This has led to a greater understanding in the effective content of well-known objects and proofs in classical computability theory. When considering the punctual anaologies of classical computabilitiy we often obtain strange and surprising results. I will discuss some recent work in progress in this area, focussing particularly on structural results. URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html  

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Date/Time : 18 Aug 2021 16:00
Venue : via Zoom
Speaker : Yu Liang, Nanjing University

Join Zoom Meeting https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Passcode: 1729=x3+y3 Besicovitch-Davis theorem says that the Hausdorff dimension of every analytic set can be approximated by its closed subset. But the Besicovitch-Davis theorem fails for co-analytic sets under the assumption V=L as observed by Slaman. We prove that the theorem holds for arbitrary sets under ZF+sTD. We also prove that the theorem holds for Sigma-1-2-sets under Martin’s axiom. This is joint work with Peng Yinhe and Wu Liuzhen.

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Date/Time : 11 Aug 2021 16:00
Venue : via Zoom
Speaker : Frank Stephan, National University of Singapore

Join Zoom Meeting https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09 Meeting ID: 830 4925 8042 Password: 1729=x3+y3 Let a positive equivalence relation to be an r.e. equivalence relation on the set of natural numbers with infinitely many equivalence relations. Khoussainov initiated with coauthors a deep study of the following question: Given a positive equivalence relation eta, which structures from a given set of structures does this equivalence relation realise? Here realisation means that functions in the structure are recursive and relations are r.e. with the equality itself given by the equivalence relation eta. In other words, the given r.e. structure divided by eta is the structure realised by eta. Now questions studied by Khoussainov and his coworkers included questions like “What is the partial ordering on positive equivalence relations eta,rho where eta is below rho iff every structure of the given type realised by eta is also realised by rho? Besides algebraic structures and orders, it has also been studied how the learnability notions behave with respect to uniformly r.e. one-one families realised by positive equivalence relations.

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Date/Time : 14 Apr 2021 17:00
Venue : via Zoom
Speaker : Karen Seidel, University of Potsdam

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Learning from positive and negative information, so called informant, is one of the models for human and machine learning introduced by Gold. We review existing classical and recent results regarding the learning power of associated settings.

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Date/Time : 07 Apr 2021 17:00
Venue : via Zoom
Speaker : Frank Stephan, National University of Singapore

Talk via Zoom: https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? In the year 2013, Keng Meng Ng, Frank Stephan, Yue Yang and Liang Yu published the paper “Computational Aspects of the Hyperimmune-free Degrees” and one of the results was given without a proof. The current talk gives the full proof of this result. In particular, the talk provides the full details of the construction of an co-r.e.\ infinite binary tree with uncountablly many branches which are all hyperimmune-free, Schnorr-trivial, jump traceable, generalised low and of minimal Turing degree. Hyperimmune-free means that every function Turing reducible to it is majorised by a recursive function. Jump traceable means that for every e one can compute an explicit bound on the number of elements which some further set also depending on e enumerates and that finite set contains the Jump value at e. Generalised low means that the jump of A is recursive in the join of A and K. A minimal Turing degree is a nonrecursive Turing degree below which is only the recursive one. Schnorr trivial means that for every f truth-table reducible to the set there is a recursive function which lists out for each input x a set of x+1 many values with one of them being f(x).

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Date/Time : 31 Mar 2021 17:00
Venue : via Zoom
Speaker : Lars Kristiansen, University of Oslo

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? We will address the following question: Do we need, or do we not need, unbounded search in order to convert one representation of an irrational number into another representation? We will consider well known representations like Cauchy sequences, Dedekind cuts, base-2 expansions, base-10 expansions and continued fractions, and maybe a few less well-know representations.

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Date/Time : 24 Mar 2021 17:00
Venue : via Zoom
Speaker : Philipp Schlicht, University of Vienna

Join Zoom Meeting https://nus-sg.zoom.us/j/96860201432?pwd=cVdwZmd2clVFaEhaTmJjaGdXMFdmdz09 Meeting ID: 968 6020 1432 Password: Is P=NP? Abstract: While descriptive set theory studies definable sets of words of length omega, generalised descriptive set theory studies words of uncountable regular length. The talk will begin with an introduction to this field and its applications. I will then talk about how one can characterise when a definable set is small or admits a colouring with few colours with respect to an open graph. This is joint work with Dorottya Sziraki.

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