Recent Posts

April 13, 2018
Angluin's style learning for weighted automata
Nathanaël FijalkowWe show that weighted automata over the reals can be learned efficiently in Angluin's supervised scenario.This post uses all the notations of the previous post,and the result presented here was proved in this paper.The scenario is Angluinâ€™s style ...

April 12, 2018
Fliess' theorem for minimising weighted automata
Nathanaël FijalkowWe state and prove Fliess' theorem, which says that the minimal automaton recognising a given formal series has size the rank of its Hankel matrix.A formal series (here over the reals) is a function .The Hankel matrix of is a biinfinite matrix ...

April 02, 2018
The fundamental theorem of statistical learning
Nathanaël FijalkowWe state and prove the fundamental theorem of statistical learning, which says that a class of functions is learnableif and only if it has finite VC dimension.This post uses all the notations of the previous post. Theorem: If $H$ has infinit...

March 15, 2018
VC dimension, Rademacher complexity, and growth function
Nathanaël FijalkowWe define the VC dimension, the Rademacher complexity, and the growth function of a class of functions.Let $X$ be the set of inputs. The general learning question we consider is the following: we want to learn a target function through a number o...

December 28, 2017
Zielonka's algorithm for parity games
Nathanaël FijalkowThis post revisits Zielonka's algorithm.One of the point of this post is to extract from Zielonka's algorithm the notion of signatures, which is the key to the correctness proof for the small progress measure algorithm of Jurdziński.Zielonka'...

December 27, 2017
The backward approach of Muller and Schupp for positional determinacy
Nathanaël FijalkowThis post revisits Muller and Schupp's backward approach to prove the positionality of parity games.The argument is simple and beautiful; credits go to Thomas Colcombet for this presentation.We discussed the technical details of the construction i...

December 25, 2017
Value iteration for parity games
Nathanaël FijalkowThis post presents a generic value iteration algorithm for parity gamesparametrised by universal trees. As special cases this extends the small progress measure of Jurdziński and the succinct progress measure of Jurdziński and Lazić...

November 10, 2017
Separation for parity games
Nathanaël FijalkowThe postulate is that three algorithms for parity games, namely the small progress measure algorithm of Jurdziński, the succinct progress measure algorithm of Jurdziński and Lazić,and the power counting algorithm of Calude et al, ca...