Karoliina LEHTINEN - Quasi-polynomial techniques for parity games and and other problems
Institut de Mathématiques de Marseille (UMR 7373)
Site Sud - Bâtiment TPR2
Campus de Luminy, Case 907
13288 MARSEILLE Cedex 9
Karoliina LEHTINEN (University of Liverpool)
Parity games are central to the verification and synthesis of reactive
systems : various model-checking, realisability and synthesis problems
reduce to solving these games. Solving parity games — that is, deciding
which player has a winning strategy — is one of the few problems known
to be in both UP and co-UP yet not known to be in P. So far, the quest
for a polynomial algorithm has lasted over 25 years.
In 2017 a major breakthrough occurred : parity games are solvable in quasi-polynomial time. Since then, several seemingly very distinct quasi-polynomial algorithms have been published, and some of these ideas have been used to solve other automata-theoretic problems.
In this talk, I will give an overview of these developments and the state-of-the art, with a slight automata-theoretic bias.
Bibliography : Roughly, this talk is based on developments presented in
the following papers, by myself and others :
* Universal trees grow inside separating automata : Quasi-polynomial lower
bounds for parity games. W. Czerwiński, L. Daviaud, N. Fijalkow, M.
Jurdziński, R. Lazić, P. Parys. SODA 2019
* Improving the complexity of Parys’ recursive algorithm. K. Lehtinen, S.
Schewe and D. Wojtczak. Unpublished.
* Parity Games : Zielonka’s Algorithm in Quasi-polynomial Time. P. Parys. MFCS
* Alternating weak automata from universal trees. L. Daviaud, M. Jurdziński
and K. Lehtinen CONCUR 2019
* On the way to alternating weak automata. U. Boker and K. Lehtinen. FSTTCS
* A modal μ perspective on solving parity games in quasi-polynomial time. K.
Lehtinen. LICS 2018
* Succinct progress measures for solving parity games. M. Jurdziński and R.
Lazić. LICS 2017.
* Deciding Parity Games in Quasipolynomial Time. C. Calude, S. Jain, B.
Khoussainov, W. Li and F. Stephan. STOC 2017.
- Karoliina LEHTINEN